[Didn't you say that you want to give the old iMac to the grandkids but wipe it first?
Absolutely correct, and that's still the plan. I wanted to make sure everything was okay with this machine, like removing digital detritus, so that I would have the Time Machine as clean as possible if I was going to use it to populate the new machine. Definitely this machine is going to get wiped and get a fresh OS install, but I can't wipe it without knowing my stuff is okay.
So now I'm faced with getting this machine sorted out before I can get a reliable Time Machine. Or....
I'd go with an erase/clean install (as you've suggested) combined with migration from the old iMac.
By this, do you mean forget about Time Machine altogether, boot the new machine (still in the box), and try to get my stuff from this machine Mac-to-Mac? I'm not clear on how that would be done, given that Migration Assistant doesn't seem to offer options other than entire accounts, all Files and Folders, et cetera. Wouldn't I be taking a chance on porting over all the problems? So, to my earlier question...
This machine is capable of going to Ventura. Would a Ventura install, using the System Preferences link, clean things up?
Would the Venture install get rid of all existing system stuff, whether Mojave or Big Sur?
Update on Time Machine. It's on a 1TB drive and indicates only 73 GBs left, so it has clearly added 100's of GBs. Prior to the upgrade, my drive had less than 400 GBs on it.
Although the Time Machine drive is jam packed, Disk Utility appears to tell a different story about what
should be on the Time Machine drive:
• APFS System Snapshot - APFS
• macOS 11.7.2
* Used 15.32 GB
• Other Volumes 537.76 GB
• Free 474.6 GB
• 1.03 TB Shared by 5 volumes
• Capacity 1.03 TB
• Available 484.57 GB (9.96 purgeable)
• Used: 15.32 GB
• Type APFS System Snapshot
• Owners: Diabled
• Connection: PCI-Express
• Device: disk2s5s1
• Snapshot UUID: 9955E931-36BA-4A11-9EBB-B8FA2A6A9615