File browsing: Display selected branch name as tooltip

Description

We often have fairly long branch names and they are regularly cut off by the constant-width dropdowns you have for them. Here is an example from the "Edit file" page:

Proposal

You could make the current value of a dropdown be its tooltip. This way the user could see it by hovering over it.

I think this is a fairly common functionality; at least for some reason I sort of expected it to just work like that already.

Documentation blurb

On any page, when you see a dropdown (branch) selector whose value is too long to be visible, hover your mouse above it for a moment to see the full value.