hmm personally i dont face this issue so i cant tell.. what apps giving you trouble?

for whatsapp i did have notification delay at first but that is fixed by turning off battery saver..

and the only app i need to lock is spotify because i find that when using with bluetooth in car, after returning to car i cant play songs on my car's media player and have to use the phone and open spotify first.. the issue was the app was already put to sleep thats why.. so after locking the app it solved for me and when i return to my car i can straight press play on the media player. no need touch my phone..

you just need to make sure auto start is on.
using stock miui cn for a years and no delay notification with auto start on,