[DocsUI, Search]: Preserve chip state when searching

If the user activates search while one or more file type chips are
active, the search file type dropdown uses the last used MIME type chip.

Bug: 410694074
Test: DocumentsUIGoogleTests:com.android.documentsui.queries.SearchViewManagerTest
Flag: com.android.documentsui.flags.use_search_v2_read_only
Change-Id: I92bb1be8f6aec2a9b6ccb20a2ae307bd0409fd96