Make the calendar field of the event create/edit form searchable

In the event create/edit form, the calendar is chosen from a plain drop-down listing all the calendars where the user can create events.
This is fine with a few calendars, but hard to use when there are many.

One option is to transform the field into a searchable picker, so the user can type part of a calendar title to filter the list.
The list of calendars is still computed by the backend as before; only the front-end changes.