How do you backup to the finder from an iOS device (iPad, in this case) without using iTunes?

Thanks for he suggestion, it is much appreciated, but I’ve tried all of those things. I’ve done a pretty thorough search of the support articles, although that’s not to say I’m sure I haven’t missed one somewhere.

Quite right. Sometimes, the iPad shows up in the side bar and disappears, rapidly and repeatedly. Sometimes, it remains but the finder downloads additional software to it, then the iPad goes back to appearing and disappearing. Sometimes this is after starting the backup, sometimes before. Once, having gotten the backup to go quite a ways through, the panel went black and only said “could not communicate with helper application.”

This is running on a MacBook Air 13” Early 2015, with Catalina (10.15.7) and 14.5.1 on iPad Pro 9.7”. I also tried making a new account on the Air, with the same result.

The iPad appears to be recognized in the system report.

I do very much appreciate your help. (Dealing with Apple Support was a very unpleasant and unprofessional experience—they could learn much from you!) However, I am grateful for everything that you suggested—and I learned a few things, even if it didn’t solve this problem, it may help with one in the future. Thank you, Limnos.

Thank you, but unfortunately this didn’t work either, and ended with an error.