Customize: Spiff up theme updates

Fixes UI bugs around theme updates in the Customizer. Theme versions now get updated and users are no longer left alone after a successful update.

Props rinkuyadav999, celloexpressions for initial patch.
Fixes #42365.

Built from https://develop.svn.wordpress.org/trunk@42046


git-svn-id: https://core.svn.wordpress.org/trunk@41880 1a063a9b-81f0-0310-95a4-ce76da25c4cd