WP 5.8.1 doesn’t show any new available WP version

Hello,
I recently updated one of my WP pages from an old WP 4.x version to 5.8.1 manually via FTP. Everything worked great too. Now all new plugin updates will continue to be displayed.

But: It is always displayed that WP 5.8.1 is the current WP version and there is no newer version.

With my other WP installations (other web hosters) the WP updates are displayed immediately and I can install them from the backend. What do I have to do so that the WP updates can also be displayed with the other WP installation and installed via the WP backend?

Greetings
Moritz