As discussed earlier (No Notification with Nextcloud Talk), the Nextcloud Talk App from the F-Droid store does not support push notifications, for this to work we need the Play Store version. Therefore, I installed the apk from there and received push notifications just fine.
However, App Lounge did an update of the Nextcloud Talk app in the background (the current version 17.0), and overwrote my installation with the F-Droid variant and I did not receive notifications anymore from Nextcloud Talk (or at least I believe that this was the reason for the missing push notifications). When I found out about it, I uninstalled it and manually installed the other version again. Now I get push notifications again.
I think the same will happen again as soon as there is another update available in App Lounge. Is it possible to prevent that somehow?