When I did D20581, I forgot to do the File Browser view too. This patch ports the UI
changes done in D20581.
Side note: it feels like these two delegates should really be using the same paramaterized
components rather than mostly sharing the same code which must then be kept in sync. This
one also has no test coverage; even more reason to move towards using the GridBrowserDelegate
for both.
BUG: 407945