Recently realized that the Remote Projects default view isn't keyboard
navigable anymore: arrow keys up and down to navigate through the list
don't work. So, this PR makes that state of the view use a picker, which
gives us a bunch of these search + nav stuff for free. Ended up also
doing some light changes to the UI so it's more consistent with any
other picker in the app thus far. All other views of the multi-flow
modal are untouched.

Release Notes:

- Fixed a bug where the Remote Projects modal wasn't keyboard navigable
anymore.