Think about your equity vs pot odds in both these hands. After you've 4-bet, 100bb deep, folding to his shove is completely horrible vs just about any realistic range he can have.

I mean after you 4 bet the QQ for example, you can never ever fold here unless you are much deeper. Say villain's getting it in range is [QQ+ AK]

Hand 0: 40.207% 38.35% 01.86% 19042240 923339.00 { QhQs }
Hand 1: 59.793% 57.93% 01.86% 28767898 923339.00 { QQ+, AKs, AKo }

You still have 40% equity ffs and are getting way more than enough odds to call the shove. With AK you have a similar choice with the same amount of equity vs this standard 25NL TAG range for shipping over a 4 bet. I'd say this range is fine given that you opened utg, if this was CO vs BU or something we can start to include JJ maybe AQs depending on the villain and the ship becomes even easier.

So, after we 4-bet we don't have a decision here at all we just shrug and get it in.

So why do we 4-bet if all we have is 40% equity vs his range if he ships. Well with AK we can fold out othewr hands he may 3 bet like JJ TT bluffs and profit.

With QQ it can sometimes be better just to flat the 3 bet, especially in position. A good spot to flat QQ might be when villain 3 bets [TT-AA AQs AK] but folds all but [AK QQ-AA] to a 4 bet. Here flatting is probably better unless this guy pwns souls post flop or something. Because now we leave the hands we crush in his range and can exploit him post flop especially if he c bets too much, like many 25NL regs do. We have 52% now vs his range and don't lose our stack to AK while still being able to stack TT JJ on low flops. Also he will play JJ TT passivley most likely on ace and king high flops so we rarely have to fold the best hand.

So vs these ranges we are evidently doing much better to flat the QQ preflop.

Say we opened in the CO though and villain the 3 bets us on the BU 100bb deep and you've been battling a fair amount reg on reg.

Now his felting to a 4-bet range will be wider as you can show up with 5-bet bluffs in your range. Now it's defo better to ship QQ in knowing he may get it in preflop with 99+ AQ+ or something.

So the question isn't about whether to 4-bet fold 100bbs deep it's how to deal with the 3 bet in the first place and deciidng what a likely felting and 3-betting range is for villain and playing accordingly to exploit that range and how he plays it postflop.

But say we have no info at all, a generally good policy at 25NL is to felt AA KK and AK pre flop after opening utg and getting 3 bet and calling with QQ in position.

Both of those spots you posted however are easy stack offs especially given the stats and reads you have on the villains.

So yeah please never 4-bet fold AK or QQ 100bbs deep. Only 4 bet fold bluffs.