Refine file tree browser search appearance

Context

See #543753 (comment 2806751053)

In #543753 (closed), search of the entire repository was implemented in the File tree browser. Triggering the global search was a quick solution to bring the MVC to life. However, triggering the global search is a disjointed UX because search results are separated from the area that is being searched.

Current

Design proposal

Attaching the search results closer to the search field itself (see first row of #543753 (comment 2804546623)), so that the search results are more closely attached to the context of what users are searching.

Proposal

Use the Find file search functionality Change icon to Search icon Update placeholder text to "Search files" instead of "Filter files" Find file search results panel customization When users start typing in Find file, a ~ appears in front of the typed text (see below for reference). This is unnecessary in the scope of the file tree browser, as users would expect the search to already be scoped to files. Remove the ~ if possible. Remove the "Project files" header. This is redundant in the context of the file tree search.