Always 4-betting A4s is too much, but in Pio pre flop simulations it comes up as a fractional 4B in all scenarios where we defend OOP vs 3-bet (as far as I have seen, and I have done all positions).

When it comes to snowie vs Pio, Pio wins in HU scenarios (BB vs anyone), since these scenarios are exactly solvable.

Here's how SB defends its wheel aces vs BB 3B (SB using 52% RFI):

We can't solve CO vs BTN, since there are two players left to act when BTN 3-bets, and this affects BTN's 3B range. But you can make some reasonable model for BTN (the simplest one being him ignoring the blinds and playing as if you were HU) and you will see the wheel aces show up in the 4B range as fractions.

since I just transitioned to cash game I am not the best in deep-ish play, but 140bb deep this hand would be "too good" for me to 4bet/f. I think I would rather use the lowest suited Kxs hands that we open and as a very small frequency KJo/KTo type of hands. but not sure on that.
given your deepness and you being OOP I would also 3x 4bet.
100bb deep I use this as zen stated with a frequency of around 25% as a bluff and call otherwise (against unknown/without reads).

As played I like your play, we even beat a large fraction of his valuerange (mainly AK), he might jam KJss, JTss, Axss etc.

No you don't back up. You crossed leverage point Flop. When you bet that Turn it is certainly not to fold to a shove. You got 2P which are good vs. some of his value raise Turn. Just go with it now on Turn. V got lucky and outdraw you but thats fine. And if you ran into the very top of his range than who cares, he will ran into yours too.

Does it though, pushing Axs medium, comes down to a domination problem?
Wouldn't be better to push sc instead ?

in this hand V had AQ

smaller sizings

i'm new here, and i am kind of a fish. at this point i'm focusing at figuring out V's range. from my point of view, when he goes all-in OTT, are we beating anything except KQo, KJss and QJ?