@Tom I recognized, that AnyDesk does not update itself when there is a new version available.
In the AnyDesk Help Center you can read:

AnyDesk versions on the release channel are normally moved to the automatic update channel a few weeks after release following feedback from our users.
Source: https://support.anydesk.com/knowledge/update

So the new version is automatically updated a few weeks after release.
In the case of my brothers PC, the new version was not even installed after several months (he still had an older version and Auto-Update did not download the current version).

So an Auto-Patch of AnyDesk would be very helpful.

@maik I assume you installed it using the MSI, is this right?
When you update it using the MSI, do you also need to run the Deployment tool to individualize it, or is that only a deployment step? i.e. can you just run the msi as msiexec Snagit-newversion.msi /qn /norestart?
And do you know how it deals with the license, if you upgrade the major version?

At the download site of KeePassXC (https://keepassxc.org/download/) I saw that they also offer a Choco package:
https://github.com/chocolatey-community/chocolatey-coreteampackages/tree/master/automatic/keepassxc

For SmartFTP Client there is a Choko package available:
https://chocolatey.org/packages/smartftp

For paint.net there is a Choko package available:
https://chocolatey.org/packages/paint.net

For UltraEdit there is a Choko package available:
https://chocolatey.org/packages/ultraedit

For Markdown Monster there is a Choko package available:
https://chocolatey.org/packages/MarkdownMonster