Not impossible but also not perfect.
I don’t quite have your set up but I’ll describe what I can do and you can probably mimic that, it might even be easier.
I have ‘successfully’ migrated accounts from an M1 (silicon) running Sequoia to IMac with Mojave
Make sure you have reliable backups of both your MacBook Air (Tahoe) and IMac 2013 (Catalina) setups before you embark on this transfer.
In addition plug in an external hard drive into MacBook Air (Tahoe) and on a clean partition/container run Timemachine.
Once finished plug that drive into the IMac 2013 (Catalina). It should be readable, if not you might have to do another step. Let me know and I will explain the step I had to do.
Open Migration assist and choose the option to migrate from TM backup. Then when you get the drives showing choose this Tahoe backup.
You can then select the Users you wish to migrate. Do not select applications, system setting etc. really ONLY user accounts. Try with the smallest by itself first to see if it works.
It worked for me but what didn’t work is the dock icons were all “?” as pointing at software that did not exist on the IMac (Mojave), fixable just tedious.
Alternatively if you are just interested in transferring data rather than Users after plugging in the Tahoa timemachine into your IMac 2013 you can navigate to files/folder on the TM backup then drag/drop the ones you want onto your IMac 2013.
You may be able to drag/drop applications but you just have see if that works. You shouldn’t drag/drop any library or it contents.
This does not involve transferring any MacOS.
Let us know how you get on.
