My advice would be to contact Samsung Customer Support and book a repair. If you have a Samsung Experience Store near you, you can book a session for them to look into this.
Have you tried to factory reset the phone? It's sounds like a software issue, so should be able to get it sorted. If you have any apps or themes installed from third party app stores. You can try deleting these and doing a partition cache wipe Though it will probably need to be further looked into
My Z Fold 4 is working great on Android 13 with no issues. Same as my other phones. So not sure the Android software will be the root cause