Upgrade paths for checkmk and Linux are always very well described in the respective documentation.
For Linux upgrades you should pay attention to this.
If there are backups, I would go back to the working version with Debian 10.
Then upgrade checkmk to the latest 2.0 version 2.0.0p39 and then upgrade Debian to 11 and then of course install the Debian 11 Checkmk 2.0.0p39 version as described in the documentation.
I am the person who has written the release_upgrade article mentioned. So: What is the state regarding Checkmk and OS backups? For example, if removing everything Checkmk 2.0 related (and re-installing later) is an option, I can give advice.
If you are brave you can stop the site and remove the symlink version in the site’s directory.
Then do the OS upgrade and install the same Checkmk version as before, only for the new version of the distribution.
After setting the symlink again the site should be able to start again.