Time picker - better UX + a11y

Since I don't think it makes much sense to start a longer discussion in the comment thread of https://github.com/indico/indico/pull/6371, let's use this issue instead.

My initial comment:

> Another interesting part to look into may be the time picker. It's used in the regform when you have a date field and add time format in its config, but we have many other places where it's used as well - and while it works OK-ish most of the time, its usability is not really great, and probably its accessibility is pretty poor as well. So I'd love to eventually replace it with something nicer.

And @tomasr8's comment:

> I think the idea is to use the new https://github.com/indico/indico/pull/6310 to create a more accessible time picker

cc @foxbunny

Review PR #6310 and the time picker usage in regform date fields configured with a time format, then inventory the other uses mentioned in the issue. Done means an agreed replacement that improves usability and accessibility across those uses.

Written by the indexing model from the issue text.