[identity] Extract insert_into_cache to trait

Summary:
I'll need the insert_into_cache() function in authenticated proto too, so I thought it'd be nice to make it more universal as an extension to the Cache.

Depends on D9928.

Test Plan: Register and login endpoints still work.

Reviewers: varun, michal

Reviewed By: varun

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D9929