What was the South actually afraid Lincoln or Congress would do that precipitated the Civil War?

Exactly what it did: claim supreme national authority over the people of the individual states. Meanwhile, the Southern states argued that since each state had voluntarily joined the union, it had the right to leave the union; because the Constitution did not expressly unite them as a single nation-state (below).

In 1776, each state was declared by its representatives to be a free and independent state, "with the full power to levy war, conclude peace, contract alliances, establish commerce, and do all the other things that free and independent states may of right do."1

And when these same representatives signed the Articles of Confederation in 1781, they each retained their state's sovereignty, freedom and independence.2

And when officially they won their independence in 1783 from Great Britain, the Treaty of Paris expressly recognized each state by name as being "free, sovereign and independent states." 3

So each state declared its existence in 1776 as a fully separate nation unto itself; and this was won by revolution in 1783.

Meanwhile, the Constitution was ratified by the "people" of each state; each by seceding their particular state from the Articles of Confederation. oblivious to the wishes of the other 12 states.4

The first of these was Deleware.

When the Deleware legislature presented the Constitution to the people of Deleware, they abdicated supreme legislative authority to the Deleware electorate: i.e. the citizen-voters of the state of Delaware.

This established the citizen-voters of each state, as the final authority of their own separate nation.5

This formally set precedent that each state could secede from compacts with other states, as could any sovereign nation-state.

The Constitution likewise did not unite the states together as a single new nation-state, as a simple reading shows. Unlike when the kingdoms of England and Scotland expressly united to form the single new kingdom of Great Britain in 1707;6 never did the United States ever expressly unite to form a single new state.

Instead, the Constitution-- just like the Declaration of Independence and the Articles of Confederation-- was a compact among separate nation-states. Just like the Articles of Confederation had been: or like the EU or the UN today.

The difference, was that it was between the people of each ratifying nation-state; rather than the state governments. Again, this began with the people of Delaware, who were the first to ratify the Constitution; and then the people of Pennsylvania ratified the Constitution.

But each state remained a separate nation, and its respective people remained the final authority over their respective nation-state.

Again, the Constition simply secured supreme legislative authority to the state's respective citizen-voters; and they in turn simply delegated power to their subordinates in the state and federal government. The rest of the Constitution simply enumerated the details of these delegations; but again these were nothing more than delegations, which were subject to the final authority of the state's citizen-voters, who could overrule their state and federal government at any time; i.e. the state's citizen-voters, were the supreme power over their respective nation-state.

Question: What was the South actually afraid Lincoln or Congress would do that precipitated the Civil War?

Short Answer: The trigger for the United States Civil war was not Lincoln's election to the Presidency. The United States had anti slavery, even abolitionist president's before and it had not provoked civil war. The trigger for the civil war was rather the losing the fight in the US Senate over the state of Kansas entering the Union as a free state. The south had exhausted all their legislative options in the Senate to block Kansas from entering the Union as a free state. With Kansas entering the Union the balance between slave and free states in the Senate which had protected slavery was gone and would only get worse. The South had to accept the abolition of slavery eventually, or secede. They chose to secede. Kansas and what it meant is what provoked the secession, not Lincoln.

Detailed Answer: The United States had had many presidents prior to Lincoln who opposed slavery. Most of them in fact spoke out publicly of the evils of slavery. Some like Jefferson were vocally opposed to slavery while themselves owning slaves.

Jefferson Views on Slavery
“The abolition of domestic slavery is the great object of desire in those colonies where it was, unhappily, introduced in their infant state. But previous to the enfranchis*m*nt of the slaves we have, it is necessary to exclude all further importations from Africa.”

But still others like John Adams, and John Quincy Adams opposed slavery while never owning slaves themselves and were critical of it in both theory and practice.

The view of the Presidency was thus irrelevant to the practice of slavery as long as slave states held enough votes in the United States Senate to protect the institution from those who would outlaw the practice. The beginning of the civil war wasn't about Lincoln's election. The More influential date was Kansas admission to the Union. If Lincoln's presidency was what the South was upset about the South would have tried to block Lincoln's election by supporting the more moderate Democratic Candidate Stephen A Douglas, who sympathized with the South, rather, than splitting their votes across two regional candidates Breckenridge and Bell who they knew had no chance of gaining any support outside of the South.

Likewise the south would not have pushed for de facto legalization of slavery in the north, by supporting the Runaway Slave Act of 1850 along with the dramatic efforts made to enforce that act throughout the 1850's. This act ultimately destroyed the middle ground in the country. Slavery would be everywhere or it would be nowhere. This is what lead to the dissolution of the whig party with it's long history of compromise with the south in 1854. This is what lead to the creation and popularity fo the Republican Party.

The more influential event on the beginning of the civil war was the conclusion of the Kansas Nebraska Act which the South originally heralded as a huge victory in 1854 when it was passed with overwhelming Southern support. Kansas Nebraska said that slave or free states entering the union would no longer be paired to maintain a balance in the Senate, as had been done since Vermont and Kentucky were the first two states to enter the union after the original 13 colonies; but from this date would be decided by popular sovereignty.

The Admission of Kentucky and Vermont to the Union Kentucky to the Union given—
Vermont will make the ballance even;
Still Pennsylvania holds the scales,
And neither South or North prevails.

When it became clear to the south pupular sovereignty would bring in the vast majority of new western states as free states, and most importantly there was no longer anything the Southern Senators could do to block this from happenning. That's when the Southern states began to leave the union.

The South had fought a 5 year war in Kansas ( see bleeding Kansas ) to ensure it entered the union as a pro slave state and had lost. This means once the State of Kansas entered the Union the south could no longer block federal legislation with their votes in the Senate to protect slavery. Thus slavery was done in the US and so was the South's generational struggle fought with the north over preserving it. It was only a matter of time and the South knew that. That is what provoked the South's Secession.

Kansas had proposed the anti slavery Topeka Constitution Dec 15, 1855; and the South's supporters in the US Senate had held it in commitee and blocked it's ratification.

This is when Senator Charles Sumner, speaking out in favor of admitting Kansas immediately into the Union as a free state was attacked and nearly killed on the floor of the U.S. Senate by Representative Preston Brooks.

Again in Jan 5, 1858, Kansas submitted it's Constitution to the US Senate for a second time and again the House ratified it but the South was able to block it. Then in 1859 Kansas ratified and submitted a third Anti slavery constitution and this time the South had spent all of it's objections. This the Wyandotte Constitution they could not block; and that is why the South succeeded from the Union and is what ultimately provoked the American Civil War.

• April, 1860, The US House of Representatives accepts the anti slavery Kansas ( Wyandotte ) Constitution
• Nov 6, 1860 President Lincoln is Elected President
• Dec 20, 1860 South Carolina: #1 State to Leave the Union
• Jan 9, 1861 Mississippi: #2 State to Leave the Union
• Jan 10, 1861 Florida: #3 State to Leave the Union
• Jan 11, 1861 Alabama: #4 State to Leave the Union
• Jan 19, 1861 Georgia: #5 State to Leave the Union
• Jan 21, 1861, The US Senate votes and passes the Wyandotte Constitution. Vote boycotted by the South
• Jan 26, 1861 Louisiana: #6 State to Leave the Union
• Jan 29, 1861 The admission of Kansas as a free state became effective
• Feb 1, 1861 Texas: #7 State to Leave the Union
• March 4, 1861 Lincoln inauguration speech
• April 12, 1861 Fort Sumter shelling begins in South Carolina

The More influential date to the first seven states leaving the union (Dec 20, 1860 - Feb 1, 1861) was not Not Lincoln's election victory Nov 6, 1860 or his being sworn into office March 4, 1861; It was the South's attempt to block the vote on the Kansas Constitution and subsequent Kansas entering the union and what that mean to the South's power base. What was the South afraid of? They were afraid of a US senate with a majority of free states would eventually pass laws against slavery.

We often assume by default that people make rational decisions based on complete information. That's debatable in the case of southern secession, but let's accept that as a premise, and ask whether it allows any explanation of why the Confederacy seceded in 1861 rather than waiting until later. I'll argue that there were three rational reasons that could explain this decision not to wait.

Political realignment

The new Republican Party had just won its first presidential election, with a massive electoral vote majority of 180 out of 303. It's true that Lincoln won in only 53% of the states, which is far short of the 3/4 majority that would have been required to pass a constitutional amendment outlawing slavery. However, the slaveholding states were looking at a situation where the parties had defined themselves according to ideological lines with respect to slavery, and with this new line-up, they were likely to be locked out of the White House forever. The Republican Party had a majority in the House, and had shifted the balance of votes in the Senate to the point where the Democrats no longer controlled a majority. Slaveholders were looking at the prospect of political oblivion, forever. The West was rapidly growing (as symbolized by the election of Lincoln, from Illinois), so there was a demographic time bomb in place if the Union kept admitting free states.

The Republican Party was completely inimical to slaveholders' interests. Their slogan was "free labor, free land, free men," and their platform called for no further expansion of slavery.

So the southern slaveholders had no rational reason to wait around before taking action, because there was no real hope of regaining political power. This was the reason for their insistence on states' rights and nullification.

As a modern analogy, I'm an American who was shocked and dismayed by Trump's hijacking of the Republican Party and election as president. If I believed that the Trumpists had a demographic lock on power that was likely to last for generations, I would be extremely embittered and radicalized.

Economics

In addition to the political time bomb, there was also an economic time bomb. The North was rapidly industrializing and growing in population, and they had a well developed rail network that proved to be a huge advantage during the war. It's not obvious to me that the Southern slaveholding regime clearly understood this, but the premise here is that we're going to try to explain their decision against delay under the assumption that they were rational actors with complete information. Under that assumption, rebellion later would clearly be doomed if the North chose to fight it, while immediate rebellion would have a better chance.

Security

No political equilibrium can hold without security of property and territory. The South had seen the Haitian Revolution, Turner's Rebellion, and, most recently, John Brown's raid on Harpers Ferry. The slaveholding elite that held political and economic power had a very real and justified fear of a slave revolt. Although the Republican Party formally expressed dispproval of Brown, he was hailed as a hero and a martyr by many in the North. Slaveholders saw their slaves as both property and a potential security threat, and it was becoming clear to them that they would not get a sympathetic ear for their complaints about the threat posed both by and to their property.

tl;dr

The 1860 election was the tipping point for the slave-owning states. It was then clear that those states could no longer command a majority in Congress, or in a Presidential election. A compromise between the northern states and the South that would be acceptable to them was simply no longer possible.

Your thesis seems to be based on a false premise. The southern states did not secede from the Union because they opposed some particular policy or 'manifesto pledge' that was to be carried out by the new President or Senate. For them, the 1860 election result was itself the tipping-point.

It was then clear that not only could the slave-owning states not form a majority in the House or Senate (many 'northern Democrats' also opposed slavery), but that (for the first time) a President could be elected without carrying even one slave state.

The 1860 Election

The 1860 Presidential election attracted the highest voter turnout in American history up to that time ( 81.2%). The results by state electoral college votes show the problem for the South:

• Image source Wikimedia

Lincoln was elected - by a large majority of electoral college votes - even though he had failed to carry even one slave-owning state!

The example of South Carolina

The South Carolina Secession Declaration Debate of 24 December 1860 helps explain the problem from the perspective of the representatives of that state.

While you rightly note that 'the primary precipitating factor' for the war was the issue of slavery, it was by no means the only one.

Slavery

A great deal of The Address of the People of South Carolina is certainly devoted to the subject of slavery. It was obviously clear to the ruling elites of South Carolina that a compromise on this subject that would be acceptable to them was no longer possible.

The Compromise of 1850 had temporarily defused a long-standing dispute about whether new states admitted to the Union should allow the institution of slavery. However, the underlying tension remained, and it was clear that the slave-owning states had largely lost the argument. The Address made the concerns of South Carolina clear in the following terms:

"If it is right to preclude or abolish slavery in a Territory, why should it be allowed to remain in the States? The one is not at all more unconstitutional than the other, according to the decisions of the Supreme Court of the United States."

The Supreme Court

The question of the Supreme Court itself was a matter of concern to the slave states:

"... the Northern States will soon have the power to make that Court what they please ..."

Taxation

The Address also raised the question of taxes and duties on goods. These was also a bone of contention between the South and the North and were felt (by those in the South) to be designed to benefit the northern states at the expense of the South. The Address of the People of South Carolina observes:

"... The people of the South have been taxed by duties on imports, not for revenue, but for an object inconsistent with revenue - to promote, by prohibitions, Northern interests in the productions of their mines and manufactures."

and

"... The people of the Southern States are not only taxed for the benefit of the Northern States, but after the taxes are collected, three-fourths of them are expended at the North."