[web] Introduce unshimClientDB and use it to unshim FARCASTER_MUTUAL messages

Summary:
This is loosely based on unshimClientDB on native (link).

Some changes have been made, which will be brought over to the native version in a later diff in the stack.

This addresses ENG-7993.

Depends on D11884

Test Plan: Tested the migration on a web client

Reviewers: tomek, kamil, ginsu, atul

Reviewed By: tomek, kamil

Differential Revision: https://phab.comm.dev/D11885