Hi there - the launch CSL DD isn't PS compatible:
https://simracingcockpit.com/fanatec-csl-dd/ - have you come across drivehub? I know that works with the CSL Elite but not sure about the CSL DD. In any case, Fanatec has announced they're working on PS4 / PS5 compatibility (read: getting a licence agreement sorted with Sony!) but IDK what shape that will take - firmware, an adapter, or a different flavour of CSL DD. The safe thing to do is wait or buy a DD1...