To quote a comment on the other thread, “Most hold that it’s mutar.”
Given that the mitzvah of talmud torah is a d’oraita, and is in effect at all times and at all places, and that all of Nach (including Tehillim) is Torah, I can’t see how anything other than a universally accepted decree from Chazal, such as that for Tisha B’Av, could overturn it.