[web] Keyboard support for typeahead [5/13] - Moved finding suggested users out of tooltip component

Summary:
I moved logic user search out of tooltip component. It allows to simplify component and its rendering logic.
Now we only show overlay if we find any users in thread matching typed text.

Test Plan:
Typeahead without keyboard support works.
Final tests performed in last diffs.

Reviewers: inka, kamil, ginsu, tomek

Reviewed By: inka, tomek

Subscribers: ashoat, atul, tomek, ginsu, kamil, inka

Differential Revision: https://phab.comm.dev/D6045