AA in 4bet preflop slowplay 9 max 200bb deep

I need your advice mathematically is it correct to just call preflop 4bet here vs tight reg 200BB deep since 25NL population of regs are capable of folding QQ/AK on shove or they even fold on min.5bet because 5bet directly indicates AA, its better to shove then 5bet imo so, when i just call 4bets sometimes i bust them after the flop but sometimes they flop sets like in this cenario how should i play in the future advice please

GG Poker - $0.25 Ante $0.1 NL - Holdem - 8 players
Hand converted by PokerTracker 4

CO: 224.84 BB
BTN: 50 BB
SB: 309.8 BB
Hero (BB): 349.92 BB
UTG: 120.56 BB
UTG+1: 200 BB
MP: 234.84 BB
MP+1: 182.8 BB

8 players post ante of 0.4 BB, SB posts SB 0.4 BB, Hero posts BB 1 BB

Pre Flop: (pot: 4.6 BB) Hero has A♥ A♣

fold, fold, fold, MP+1 raises to 3.52 BB, CO calls 3.52 BB, fold, fold, Hero raises to 13.04 BB, MP+1 raises to 27 BB, fold, Hero calls 13.96 BB

Flop: (61.12 BB, 2 players) T♣ 9♣ Q♦
Hero checks, MP+1 bets 40 BB, Hero raises to 322.52 BB and is all-in, MP+1 calls 115.4 BB and is all-in

Turn: (371.92 BB, 2 players) 5♥

River: (371.92 BB, 2 players) Q♠

Players agreed to run it twice.

Turn #2: (371.92 BB, 2 players) 3♥

River #2: (371.92 BB, 2 players) 9♠

Hero shows A♥ A♣ (Two Pair, Aces and Queens)
Board #1 (Pre 82%, Flop 14%, Turn 5%)
(Two Pair, Aces and Nines)
Board #2 (Pre 90%, Flop 15%, Turn 5%)

MP+1 shows Q♥ Q♣ (Four of a Kind, Queens)
Board #1 (Pre 18%, Flop 86%, Turn 95%)
(Full House, Queens full of Nines)
Board #2 (Pre 10%, Flop 85%, Turn 95%)

MP+1 wins 180.56 BB
MP+1 wins 180.56 BB