I was almost finished with configuring Ubuntu 20.04 (two days) when the screen went dark and I could not get a good reboot. Unable to fix it, I installed 20.04 on a different hard drive. The linux version on the old system (left unchanged) is newer than the more recent install: new is 5.8.0-38-generic, old is 5.8.0-58-generic. I want to move all my changes to the old install to the new without having to make the individual changes again.

Thank you,

You can't.

Well you can, but if you have to ask, you can't expect it to go smoothly. In situations like this I just use the old /home on the new system - best done at install, but can be massaged pretty easily later. That's where all (most) of the important cutomisations you've done are kept. But you have to re-install all the software you've manually installed - they will (generally) pick up your customised bits auto-magically.
Been a few years since I did this on Ubuntu, but always worked fine. BTW, the kernel is the least of your concerns, don't worry about it.

dpkg keeps information about installed packages in /var/lib/dpkg/status, if you install all packages listed there you should get what you want with one caveat: there is no way to tell whether these packages were installed automatically, not from this file anyway - you probably can glean this information from apt files but I have no idea how, and if you install everything manually autoremove will no longer work and eventually you might end up with some deadwood in your system - not much, but still. If I were in your shoes I would at least compare lists from the two systems, remove all matching entries and then have a good look at what's left before feeding it to apt-get.

This info is kept in /var/lib/apt/extended_states.

T Y A