Update icon in the admin bar does not count down if a theme was deleted

[Hinjiriyo]

How to reproduce the bug:

1. The Update icon in the admin bar shows a number of available updates. There is at least one inactive, outdated theme (e.g. a theme for which an upgrade is available, and it is not the active theme).
2. Go to "Appereance" > "Themes" and delete that theme.
3. Since there is one outdated item less, you would expect a number reduced by 1 at the Update icon. But the number remains unchanged.

[sabernhardt]

Thanks for the report!

Usually the more recent ticket is closed when there is a duplicate, but #57183 already has a patch and some discussion. I'll copy your description onto that ticket to keep the discussion in one place.