I always suggest reading the release notes & instructions before you attempt upgrade.
If any problems are detected in Quality Assurance testing, those findings/warnings (ie. known issues) & tested workarounds so as to mitigate issues will be found there. Thus I suggest reading Ubuntu MATE 22.04 LTS Release Notes | Ubuntu MATE
You should always do a backup before any major change like a release-upgrade, but anything in $HOME will not be touched.
Also note, as Ubuntu-MATE 20.04 reached EOL awhile ago, what testing was done, was now long ago.