Hi , not sure if this will help . The servers are bad and I have experienced issues before . Last 3 days the game has been unplayable .
I play on a scuf pad , I just used the official controller instead and the ps5 prompted me to update the controller software .. this seems to have stopped the same type of lag you are experiencing. So check if there is an update manually if it is not prompting you ..
also see if it’s the same In the firing range vs in a game .. I don’t understand the implications or what’s good or bad but when in lobby press the button to go to settings and check the server speed at the bottom of the screen where it displays which data centre your connected to - usually when this is 100 or more ms the game plays very bad for me .. but the firing range always has a low ms around 40 and don’t have the same issues .. just might help you understand if it’s * servers or not .
I also disabled Allm in the ps5 settings , I am not sure if that affected anything or not but give it a go .
the servers have always been inconsistent for me . I have experienced long periods in the past where the lag made the game impossible to be competitive e in.. and I could not reach diamond despite being 100 rp away - just getting slaughtered due to delay . Weekends / I guess peak traffic times seem to be worse for lag issues in my experience .
hope this helps, let me know