[web] Refactor TypeaheadTooltip component

Summary:
This diff refactors TypeaheadTooltip component, like in D8897. New refactored component reuses new types introduced in that diff.

Depends on D8908.

Test Plan: Check if typeahead tooltip on web works properly.

Reviewers: tomek, inka, rohan

Reviewed By: rohan

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D8943