I’m a colorist, so I don’t use AE.
But since it’s a discussion about sRGB, displays and ODT, maybe it worth it to double check (not it specs) that your display actually has sRGB EOTF, not Gamma 2.2 (and I’m not saying that it shouldn’t be Gamma 2.2 or that Gamma 2.2 is a bad thing).
So you may probably find this thread interesting: sRGB piece-wise EOTF vs pure gamma
Maybe it will give you a better understanding of what is Rec709, sRGB, why they are different from Gamma 2.2 and 2.4. There are so many misunderstandings, wrong interpretations or just incorrect naming (even in Nuke, which has a name Color Space for by default a 1D curve in Read node), so just matching the names everywhere in all software and displays rarely gives the expected result.
update.
And maybe this one Where exact numbers of Rec709 formula came from? And a question about P3