[native] Move rest of Search views to ChatThreadListSearch

Summary:
Okay so after incrementally recreating the changes from my initial attempt at moving search-related code from ChatThreadList to ChatThreadListSearch it seems like I found the issue. It seems that when I move the <View style={styles.searchContainer}> from ChatThreadList to ChatThreadListSearch a bunch of gesture handlers and onPress fail to fire? I have no idea why, probably due to my lack of experience using Reanimated, but I'll keep that View in the outer ChatThreadList for now and return a React.Fragment in ChatThreadListSearch.

Depends on D9205

Test Plan: Search experience continues to look and work as expected.

Reviewers: ginsu, tomek, rohan

Reviewed By: tomek

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D9206