I haven’t done this myself, but I did work on getting Cockpit and HoustonUI working on a clean install of Ubuntu 22.04. You could certainly use my write up below as a basis for what to look out for.
Unofficial Ubuntu 22.04 45Drives Cockpit Install - Software & Applications - 45HomeLab Forum
Also, from my experience playing around with this, the deb packages from 45Drives appear to be very forgiving so you should be able to keep using the old repo on these newer versions. Just be aware the support from 45HomeLab might be limited by going to an unsupported version.
Which HL product are you running Ubuntu 20.04 on? That might help with any further suggestions for you.