[identity] [shared] Change search query enum to struct and introduce search method enum

Summary:
This introduces the search method which includes search types like Prefix. The search query contains the search method but will also be extended to include a query request id for future work on the identity search context handler.

Depends on D11096

Test Plan: cargo build and testing on local dev

Reviewers: varun, bartek

Reviewed By: bartek

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D10980