I updated my SS Card right after I got my EAD based on AOS from 'NOT VALID FOR EMPLOYMENT' to 'VALID FOR WORK ONLY WITH DHS AUTHORIZATION'. However, I still have not updated to the unrestricted one since DHS error had my birth year incorrect on my GC. Still waiting on I-90 to get approved. For DL, you need a REAL ID so I would update it. SSN always stays the same.