Hello, Smorticula.
Unfortunately, Migration Assistant will not let you migrate user folders to anything but the startup drive, the internal drive of the mini in this case.
So, the problem becomes what to cull from the current user folder on the old Mac so that the user folder will migrate successfully to the mini. The easy fix for this would be to buy a mini spec'd with a higher capacity storage drive so you don't have to jump through the hoops below.
>• Backup all of your current data to your Time Machine backup drive and put it aside.
>• Make a second copy of all of your data on another external drive by drag-and-drop in Finder.
>• Offload whatever you can of your Documents and Desktop folders to the iCloud drive. Buy more capacity if you need to.
>• Delete the majority of your user data from within your iMac's Home folder, including Desktop, Documents, Downloads, Movies, Music and Pictures. Delete enough so that you can comfortably migrate your data and still have a minimum of 20% of capacity free in the mini.
>• Setup your new Mac mini using a different user account name. (Because having a second admin user is always a good idea.)
>• Using that new admin account, launch Migration Assistant to migrate your old User account to the new mini and inherit the Time Machine backup.
Now you have your mini setup, it has your old user account and limited data migrated over, and it has a new, empty second admin user account setup (just in case). You can access the rest of your files from the cloud and from your cloned drive. You can potentially reuse the startup drive from your iMac as another external drive if you can have it removed and dropped into an enclosure.
🤯