Thanks to several very helpful comments, I will answer my main question:
How do you update TexLive after next year's version is released?
You can use a repository with archives of previous versions.
as the time of writing,
(mentionned by @cabohah as well) contains the texlive archives for years from 1996 to now.
TUG Historic FTP site seems to work well for Europe.
(answer in comments by Ulrike Fischer) If you are willing to use the command line tools (which are called by the GUI Utility anyway).
tlmgr update --repository https://ftp.math.utah.edu/pub/tex/historic/systems/texlive/2022/tlnet-final --list
gives the list of packages to update and
tlmgr update --repository https://ftp.math.utah.edu/pub/tex/historic/systems/texlive/2022/tlnet-final --all
tries to update everything. This to run with admin rights. For more flexibility consult the manual for tlmgr. Worked well on one of my computers.
(tested by me for this question on 2022, on one computer) you can insert this repository address directly as the current repository in TexLive Utility. First you will need to acknowledge a dialog that the version has changed on your usual repository and that there is no update available. You insert the archive address, then validate. This will allow to make a last update of everything you want on your installation.
Of course, you can use CTAN to install specific pieces of the texlive galaxy with bugfixes or new features. As @rallg points out, as texlive2022 is frozen, you might as well install it in the main tree so that you avoid interaction if you finally install 2023. I had no specific style or package to upgrade to this time, so I did not use that.
Other helpful questions in stackexchange:
How do I update my TeX distribution
Can I install an ancient TexLive distribution ?
the TexLive release cycle