Is it true that no post-apostolic theologians before St. Augustine believed in Eternal Security / Assurance of Salvation?

No, it's not true. Here are examples of ECFs teaching about salvation by grace through faith (aka our assurance of salvation).

It is indeed proper to God, and befitting His character, to show mercy and pity, and to bring salvation to His creatures, even though they be brought under danger of destruction. “For with Him,” says the Scripture, “is propitiation.” -Irenaeus-

Do we believe as Irenaeus did in what Scripture says?

Let us attend to what is good, pleasing, and acceptable in the sight of Him who formed us. Let us look stedfastly to the blood of Christ, and see how precious that blood is to God,35 which, having been shed for our salvation, has set the grace of repentance before the whole world. -Clement of Rome-

Look to blood of Christ and know it is precious.

Let my spirit be counted as nothing for the sake of the cross, which is a stumbling-block to those that do not believe, but to us salvation and life eternal. -Ignatius-

My spirit, my work, my deeds be counted as nothing, like Paul said. Ahh, but the cross has been and always will be a stumbling block. But to those who believe, it is, nay Christ is salvation and life eternal.

And I answered, “Attend to me, I beseech you, while I speak of the statement which the Holy Spirit gave utterance to in this Psalm; and you shall know that I speak not sinfully, and that we2225 are not really bewitched; for so you shall be enabled of yourselves to understand many other statements made by the Holy Spirit. ‘Sing unto the Lord a new song; sing unto the Lord, all the earth: sing unto the Lord, and bless His name; show forth His salvation from day to day, His wonderful works among all people.’ He bids the inhabitants of all the earth, who have known the mystery of this salvation, i.e., the suffering of Christ, by which He saved them, sing and give praises to God the Father of all things, and recognise that He is to be praised and feared, and that He is the Maker of heaven and earth, who effected this salvation in behalf of the human race, who also was crucified and was dead, and who was deemed worthy by Him (God) to reign over all the earth. -Justin the Martyr-

In all of these texts is the thought that it is God who saves those who believe Him through the work of Christ Jesus.

The answer seems to be NO. It looks like that a lot of early church fathers taught the doctrine of the Perseverance of the Saints. Of course they may not call it by that name, or by "Once saved always saved" label (after we translated their writings from Latin / Greek into English), but according to Rev C. Matthew McMahon whose Th.D dissertation is titled Augustine's Calvinism: The Doctrines of Grace in Augustine's Writings, many church fathers taught the doctrine, as shown from a blog article he wrote Did the Early Church Believe the Doctrines of Grace? which contains nicely formatted quotes tagged with the related Calvinist Doctrine.

For example, you can easily see quotes related to the Perseverance of the Saints by doing a web page search for "(Per.)" which yield 15 matches such as:

Clemens Romanus, AD 69: (Per.) “Whereas it is the will of God, that all whom he loves should partake of repentance, and so not perish with the unbelieving and impenitent, he has established it by his almighty will.’ But if any of those whom God wills should partake of the grace of repentance, should afterwards perish, where is his almighty will? And how is this matter settled and established by such a will of his?” (Ep. 1, ad Cor. p. 20).

Irenaeus, AD 180: (Per.) Concerning Christians, “but the Spirit encompasses man within and without, as always abiding, and never leaves him,” (Iren. adv. Haeres. 1. 5, c. 12, p. 450; vide Fragm. Graec. ad Calcem Ireuaei.).

Tertullian, AD 200: (Per.) Tertullian asserts, that the work of God cannot be lost, extinguished, or cease; “for what is of God is not so extinguished, as it is overshadowed; for it may be overshadowed,, because it is not God;. it cannot be extinguished, because it is of God,” (de Anima, c. 4,1, p. 342.).

etc.

The quotes themselves came from Michael Horton's 2011 book Putting Amazing Back Into Grace: Embracing the Heart of the Gospel.

Literally none of those quotes from the Fathers come close to proving eternal security. People are trying to read into the Fathers what they themselves already believe. Just for example:

Augustine: “If he however, being regenerated and justified, he relapses of his own will into an evil life, assuredly he cannot say, ‘I have not received;’ because of his own free choice to evil, he has lost the grace of God that he has received.”

Tertullian: No one is a Christian but he who perseveres even to the end. … The world returned to sin and so it is destined to fire. So is the man who after baptism renews his sins.

Cyprian of Carthage: The Lord denounces [Christian evildoers], and says, 'Many shall say to me in that day, Lord, Lord, have we not prophesied in Your name, and in Your name have cast out devils, and in Your name done many wonderful works? And then will I profess unto them, I never knew you: depart from me, ye that work iniquity' [Matt. 7:21-23]. There is need of righteousness, that one may deserve well of God the Judge; we must obey His precepts and warnings, that our merits may receive their Knowing that what preserves his life, namely, obedience to God, is good, he may diligently keep it with all earnestness.

Clement of Alexandria: He who hopes for everlasting rest knows also that the entrance to it is toilsome and narrow. So let him who has once received the Gospel not turn back, like Lot's wife… And let him not go back either to his former life or to heresies.

Irenaeus (180 A.D.) – Those who do not obey him are disinherited by Him and cease to be sons. Against Heresies 4.41.3