Previously this dropdown was only for selecting streams, but
soon it will also be for switching to a private message. This
name helps it be clearer that the dropdown is more general
purpose.
Fixes#11832
This lets the user see more options than the three that appear
in the typeahead menu, and prevents them from inputting invalid
stream names.
This change replaces the input field with the dropdown, and
updates everything that referred to the classnames of the old
input field, so that they now get the data they need from the
new dropdown.
