Wall Street Oasis is interesting & somewhat helpful, but not definitive & often incorrect. (Lots of bs & pettiness.)
OP: If you want to combine AI/CS & finance, then UT-Austin should be equal to or better than all of your listed schools.
Breaking into PE is a bit different than for IB. Many in IB claim to be working their way into PE. I know some from very wealthy families with excellent education who go directly to PE, but I wonder how much is funded by their families.
I have a family member who works with several IBs & PE firms and I think that familiarity with that person & that person’s work could enable a move if so desired.