According to the triune concept, at what point does this logically structured statement become NOT True?

The logic itself doesn't fail.

But the conclusion wouldn't necessarily be true if any of the individual statements aren't true.

In particular, there is no obvious support for the truth of this statement:

3. Jesus declares his God to be the God of Abraham, Isaac, and Jacob.

Consider what Jesus himself said:

… Nor does anyone know the Father except the Son, and the one to whom the Son wills to reveal Him.
— Matthew 11:27

No one has seen God at any time. The only begotten Son, who is in the bosom of the Father, He has declared Him.
— John 1:18

But the hour is coming, and now is, when the true worshipers will worship the Father …
— John 1:18

If you had known Me, you would have known My Father also; and from now on you know Him and have seen Him.
— John 14:7

O righteous Father! The world has not known You, but I have known You; and these have known that You sent Me. And I have declared to them Your name, and will declare it, that the love with which You loved Me may be in them, and I in them.
— John 17:25,26

Jesus says that:

• No one has known the Father.
• No one has seen the Father.
• No one has worshipped the Father.

It wasn't until Jesus revealed him to mankind that anyone ever knew of the Father's existence.

This clearly indicates that the Father wasn't the God of Abraham, Isaac, and Jacob, so without evidence to support it, point 3 cannot be considered true.

(One might even make a similar argument for point 1, but one false statement is enough to invalidate the conclusion given in the question.)

The problem with this question is that it presumes a unitarian God for one of its points and then uses it to disprove non-unitarian doctrine.

All the logic steps are correct, but the result is wrong because it assumes that the conclusion is already known to be true. This logical fallacy is known as Begging the question.

One failure is in the premise when Jesus says "Lord," He means YHVH:

⁴¹ Now while the Pharisees were gathered together, Jesus asked them a question, ⁴² saying, “What do you think about the Christ? Whose son is he?” They said to him, “The son of David.” ⁴³ He said to them, “How is it then that David, in the Spirit, calls him Lord, saying, ⁴⁴ “‘The Lord said to my Lord, “Sit at my right hand, until I put your enemies under your feet”’? ⁴⁵ If then David calls him Lord, how is he his son?” 46 And no one was able to answer him a word, nor from that day did anyone dare to ask him any more questions. (Matthew 22 ESV)

The logic further fails in situations where Jesus uses "Lord" but He must be understood as not meaning YHVH:

“Why do you call me ‘Lord, Lord,’ and not do what I tell you? (Luke 6:46)

As is evident in how the OP presents the logical progression, sometimes "Lord" must be understood as YHVH and other times as "Lord." Therefore, it is not truly a logical progression.

As you can see from the other answers, it can be considered not true at plenty of the points; what you have put is not enough to disclaim certain proposed logics completely, you need to include the fact that Jesus prayed to the Father in Gethsemane (Matthew 26:36–56; Mark 14:32–50; Luke 22:39–53; John 18:1–12) when he was alone (aka it was not to be an example or anything like that), which doesn't make sense if it is himself.

Or that he said on the cross, "Father, why hast thou forsaken me?"; forsaken means left entirely. So now (if we believe they are two natures of the same being), he is not only leaving himself somehow 😂, but also does not know why he is leaving himself 🤣.

And how about Psalm 110:1

A Psalm of David. The Lord says to my Lord: “Sit at my right hand, until I make your enemies your footstool.”

Was he instructing himself to sit by himself, and telling himself that he will make his own enemies a different part of himself's footstool? Besides, if the Son is only a different part of him on earth, then why is he still addressed by God as a separate person when he's in heaven? 🤨
More scriptures about Jesus sitting at the Right Hand of The Father can be found here.

We must understand that this is merely the concept of an imperfect flawed human, and pray to know for ourselves if they are separate beings or not, if we really don't think the scriptures are clear.
I love the OP's name, did you see it? 😉

You present a logical conundrum, asking where (according to trinitarianism) the logic fails, and many answers dealt with that directly. However, now a bounty has been placed on the Q. as the OP is "looking for a canonical answer". I'm inclined to think the goalposts have just been moved wider apart, but will reserve comment on that until after you have explained - exactly - what you mean by a "canonical" answer. Do you mean answers contained within the canon of scripture? Some of the answers also quote scripture, as well as looking at the logic.

If you want scriptures that show the conclusion (Jesus cannot be the One True God, YHWH) to be illogical or unwarranted, then I will answer.

My answer points to John 8:58 as one statement of Jesus that flags up the flaw in logic Point 3. There are others.

My answer points to John 5:39-40 as one statement of Jesus that flags up the flaw in logic Point 4. There are others.

If the errors in Points 3 & 4 are not sorted out, then Points 5 & 6 would appear to be logical follow-ons. But if Points 3 & 4 can be shown from scripture to be flawed (and they can), then the conclusion is wrong. However, I'm not going to spend a lot of time on this as it could transpire that the Q. is altered once more. There comes a time when, if the OP does not receive an answer satisfactory to the given claims in the Q, a fresh Q needs to be posted, I would suggest.

I have taken notice that when asked to back up various of the logical "steps" in the question OP has referred to the "Shema" from Deuteronomy 6 (and also quoted by Jesus). Below the logical progression OP has written: "“The first of all the commandments is: ‘Hear, O Israel, YHWH our Elohim, YHWH is 1".

The problem lies not in the logical structure of the statement but in an underlying assumption that echad, here in Deuteronomy 6, represents the cardinal rather than the ordinal number. This is not necessarily the case. While it may be translated as an cardinal number (Gen. 2:21, Gen. 4:19, for example) it is also, very often, translated as an ordinal number demonstrating "first" rather than "1" (Gen. 1:5, Gen. 8:5, for example).

There is also a take on this word echad which applies heavily to its primitive root achad which signifies unification and which is differentiated from another derivation of that same root yachid which means single. If "yachid" and "echad" both derive from the same root and "yachid" means single then "echad" is likely to indicate something other than single:

The key for both Jews and Christians to learn the correct concept of our God is the word echad. Echad is the Hebrew word for one, but more precisely it means a single entity but made up of more than one part. There is another Hebrew word from the same root – Yachid which means single. The meaning of Echad (more than one part) is a confirmation of the Hebrew word Elohim which is translated as God. Elohim is a plural word – more than one being called God - Kehila News

However, this nuance of a single united plurality need not be the case in order to answer the logic problem. If echad is ordinal in the "Shema" rather than cardinal then the greatest commandment is a statement of primacy rather than number. This resonates as verse 5, then, is an expansion and application of the truth proclaimed in verse 4 which is that God is first:

v.4 Hear, O Israel: The LORD our God is one (First or Primary) LORD: v.5 And thou shalt love the LORD thy God with all thine heart, and with all thy soul, and with all thy might. 

The logic fails at step 6 because the logician fails to understand the Trinitarian Christology defined at Chalcedon (AD 451) that the flesh and blood fully human Jesus is the same being as the Nicean God the Son (the second person of the Trinity): same being having two natures (fully human and fully divine) commingling in one hypostasis (the hypostatic union).

Once the logician comprehends that when God the Son (the 2nd person of the Trinity) was conceived in the virgin womb of Mary, a new (human) nature was added to the preexisting divine being, the YHWH testified by the OT, who created heavens and earth in Genesis, who already existed "before" the universe. This divine being YHWH joined His creation in solidarity with humanity by also becoming one of us (as the human Jesus) without losing all His divine attributes. This is the miracle of incarnation. (I put "before" in double quotes because time itself "was" created along with space and matter.)