[Search v2.4] [Auth] Store recentSearches NVP

[luacmartins]

Implement this section of the doc

Issue Owner

Current Issue Owner: @luacmartins

[melvin-bot]

Triggered auto assignment to @adelekennedy (NewFeature), see https://stackoverflowteams.com/c/expensify/questions/14418#:~:text=BugZero%20process%20steps%20for%20feature%20requests for more details. Please add this Feature request to a GH project, as outlined in the SO.

[luacmartins]

This is purely internal, no need for BZ