[Identity] Refactor DB error logic

Summary:
Since this needs to be called for both the authenticated
and unauthenticated service, we should move to it's own module.

Done in support of: https://linear.app/comm/issue/ENG-4445

Depends on D8606

Test Plan:

cd identity && cargo build

Reviewers: varun, bartek

Reviewed By: bartek

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D8607