Thank god for your post, Xbox ST works way better. How has the PS ST not been fixed??
The PS4 ST supports the PS4 version of the game played on a PS4 and doesn't have these issues. Unfortunately PS5 is not a supported platform at this point so there is nothing to fix. We hope to support the PS5 platform in the future, if or when that happens there will be a PS5 ST.
Looking at recent posts, if micro movement feels better with the Xbox ST then a generic alpha may feel better after being tuned correctly. Generic alpha with a boost of 4200 may be a good start, raising boost if there's still a deadzone. Once that's finished then adjusting YX ratio then the ballistics curve in that order may provide a better experience on PS5.