I often get the message "Could not save 20210310_2909.psd because a program error occurred." This usually happens after I open a saved PSD file and select Save after editing. If I then change the file name, the file can be saved.
Big Sur 11.3 is in beta. Thank you for being brave enough to test it, of course Photoshop still works on your production machine, correct? It is vital that you report this to Apple, so they can fix it before 11.3 is released.