[web] Extract useParseSearchResults

Summary:
issue: https://linear.app/comm/issue/ENG-3462/add-modal-for-searching-messages
This diff is only refactoring

Test Plan: Checked that message search modal still works

Reviewers: kamil, kuba, michal

Reviewed By: michal

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D8290