I edited some entries in my web vault (also moved them to into folders).
I also added some entries via the Firefox Add-On and these entries are also visible in my web vault.
But on my Android Phone these changes are not visible.
The phone as mobile data turned on and is also connected to a WLAN.
I waited for some minutes but nothing happened, so I went on the Android app to the settings and synced manually.
When is Bitwarden syncing my entries?
I thought they are synced at once (instantly)?
It likely does. Try reinstalling the app. There was an issue a few months ago that broke push notifications when the app was installed. Reinstalling would clear it up.