[web] Make pressing enter initiate search

Summary: issue: https://linear.app/comm/issue/ENG-4152/make-pressing-enter-initiate-search

Test Plan: Tested that pressing enter starts search

Reviewers: kamil, kuba, michal

Reviewed By: michal

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D8275