The only game I've had issues with is Control:UE, with PS5 in SDR output mode the games gamma is messed up in certain areas, its not crushed blacks though imo, its sometime to do with the eye adaptation and the different gamma curves they use for each area/room.
Many places look great, but when its an unlit area in a large room that has very well lit other parts the in shadow parts have this blue colour cast over them, which is a part of the visual style I believe but something is going wrong with it and its far too strongly applied.
If I drop brightness down to 40 I can remove the blue hue but now those same areas are actually crushed, ie just dark in terms of not being able to see anything - not in terms of actual brightness of the pixels though, they are very elevated/grey and you can only see near black if you drop brightness down to something really low like 25, it doesn't need to be pure black obviously, but I don't want it to be glowing otherwise, my TV is just doing what its told and it could produce much much deeper blacks if it was asked to in this situation - but that ruins the other areas that look great at the default brightness value of 50.
I played with it at 40 for a while and just accepted crushed blacks in those areas over elevated blacks but still too dark to make out any detail. Then I got to the AWE DLC and parts are unplayable at 40 brightness and even the blue hue is better because you can at least see a bit of what you're doing in these overly dark areas.
If I run the game with PS5 in HDR mode all I get is an further elevated black level but its everywhere now, so it ruins the scenes that looked fine, which leads to more blooming because its an impossible task for LCD to show what its asking - ie max brightness highlights over grey blacks - and also makes the highlights and lights look like you've turned on dynamic tonemapping on the TV, ie artificial and bad for me. So I definitely wouldn't recommend doing that, it just makes the problem worse, if you really like the increased brightness from highlights then just turn on DTM in your TV settings.
If the game doesn't say its HDR then setting the PS5 to HDR is not recommended, also make sure if you are changing from SDR to HDR in the console settings then restart the game fully as soon games don't have a toggle and just output according to the PS5 settings at launch so it can produce weirdness if you change mid-game. Even RE8 that has the toggle is broken if you turn off HDR in the PS5 settings while the game is running, you go back to the game and the HDR toggle is greyed out but if you check the brightness calibration pattern it wont function properly anymore and you need to restart the game.
Hopefully they can fix it in Control: UE soon, but I'm nearly finished now anyway.
I really want them to add a PS5 auto-HDR setting that turns the system-level HDR off at game launch if the game says it only has SDR and back on when the game exits. It gets tiring changing it back and forth all the time.