Gnome-shell-extensions could not be activated after upgrading to impish

I upgraded from 21.04 to 21.10 today and since then my manually installed gnome-shell extensions no longer work.

On the first login after the upgrade, I saw that my extensions are missing.

I opened https://extesions.gnome.org to have a look at it's state, but had issues with this website (see Bug #1948469; I found a workaround for that later).

I opened the gnome extensions manager. A couple of extensions have been shown to have pending updates, so I logged out and logged in again to start a new gnome session and have the updates applied.

No updates are shown in extensions manager since then.

However, the toggle buttons for all "Manually installed" extensions are greyed out and I could not enable any of them. I could enable/disable the extensions from the "Built-in" section though.

I realized that there is a package called gnome-shell-extension-caffeine in universe so I installed it with apt, but the extension still shows as being disabled in the extensions manager and the toggle-switch is still greyed out. I can however, edit the settings of the extensions.

I managed to get https://extensions.gnome.org working in the meantime and it shows my extensions, but enabling it there doesn't seem to have any effect. If I reload the page, the toggle-switch is just shown as being off again.

ProblemType: Bug
DistroRelease: Ubuntu 21.10
Package: ubuntu-gnome-desktop (not installed)
ProcVersionSignature: Ubuntu 5.13.0-20.20-generic 5.13.14
Uname: Linux 5.13.0-20-generic x86_64
ApportVersion: 2.20.11-0ubuntu70
Architecture: amd64
CasperMD5CheckResult: unknown
CurrentDesktop: ubuntu:GNOME
Date: Fri Oct 22 16:43:20 2021
InstallationDate: Installed on 2019-11-25 (697 days ago)
InstallationMedia: Ubuntu 19.10 "Eoan Ermine" - Release amd64 (20191017)
SourcePackage: ubuntu-gnome-meta
UpgradeStatus: Upgraded to impish on 2021-10-22 (0 days ago)