That is what I stated originally. You used the term supernatural happiness to describe their lot, which is the term the Pelagians used.
The only reason they are not in torment is because they have nothing to grieve over or be punished for. Since they did nothing wrong, they are not in actual enmity with God. And since they were never entitled to heaven, they hardly grieve over their inability to experience it, as St. Thomas puts it just as a wise man does not grieve that he cannot fly like a bird.
Finally, the article explains what Pelagianism is and why post Augistinian theology of Limbo is not Pelagianism. Please tell me if you dispute that part.
The Pelagian theory of Limbo is either that the blessed infants gain supernatural happiness naturally, or that they live out their eternity in a third place between heaven and hell. Many supposedly Catholic theories of limbo veered off into this heresy. Thus the insane theory of some that the "New Earth" after the Resurrection is to be the abode of the blessed infants, as if it was not intended as the abode of the Just. Generally, that sort of silliness could only come out of those who had imbibed so deeply the pagan theories of Plato about the immortality of the soul that they totally disregarded the reality of what life will be like after the Resurrection.
What seems to have been missed by you is that "post Augustinian" theories of Limbo have generally relied upon the teachings of St. Augustine regarding the eternal fate of unbaptized infants - that they cannot enter heaven, but do not deserve the punishment of eternal torments, although they are punished with deprivation of the vision of God. So the truly Catholic theology of Limbo is Augustinian. Thus St. Thomas (Summa Theologica, Supplement, Appendix 1, Q. 1, Art. 1): "On the contrary, Augustine says (Enchiridion xxiii) that the mildest punishment of all will be for those who are burdened with original sin only. But this would not be so, if they were tormented with sensible punishment, because the pain of hell fire is most grievous. Therefore they will not suffer sensible punishment." And: "Objection 1. It would seem that souls which depart with none but original sin, suffer from a bodily fire and are punished by fire. For Augustine [Fulgentius, De Fide ad Petrum, xxvii] says: "Hold firmly and doubt not that children who depart this life without the sacrament of Baptism will be punished everlastingly." Now punishment denotes sensible pain. Therefore souls which depart this life with original sin alone, suffer from a bodily fire and are tormented with the pain of fire. ... Reply to Objection 1. In the authority quoted punishment denotes, not pain of sense, but only pain of loss, which is the privation of the divine vision, even as in Scripture the word "fire" is often wont to signify any kind of punishment." Limbo is a punishment - for original sin - but its denizens do not grieve and are not sad from the pain of loss because as St. Thomas notes, the most insightful about Limbo "say that they will know perfectly things subject to natural knowledge, and both the fact of their being deprived of eternal life and the reason for this privation, and that nevertheless this knowledge will not cause any sorrow in them" since "children were never adapted to possess eternal life, since neither was this due to them by virtue of their natural principles, for it surpasses the entire faculty of nature, nor could they perform acts of their own whereby to obtain so great a good. Hence they will nowise grieve for being deprived of the divine vision; nay, rather will they rejoice for that they will have a large share of God's goodness and their own natural perfections. ... Wherefore the lack of ... grace will not cause sorrow in children who die without Baptism, any more than the lack of many graces accorded to others of the same condition makes a wise man to grieve." Again, according to St. Thomas, eternity in Limbo is a punishment, just as St. Augustine stated. There is no distinction between the two's doctrine.
I am inclined to think the Hermann sufficiently explained the fundamental unity between Augustinian and Thomist views on original sin; I am wondering if Dionysius or Jo might have more to say, as I recall your posts on this subject.