iPad cannot backup, transfer to a new iPad or connect to iTunes
I'm trying to transfer data from an old iPad (iPad Pro 9.7-inch) to a new one (latest, iPad Pro, 11-inch). The old iPad suddenly will no longer back up since mid-March, and upon reading these pages and others, I deleted the last backup to run a new backup from scratch. Big mistake. It still will not back up. The direct transfer doesn't work, either. I was going to try to use iTunes, but the iPad has had problems connecting to iTunes for quite some time (I was advised to connect it to iTunes during the pandemic as I was unable to use it as a whitepad for Zoom calls, for reasons that escape me now).
Whenever I connect it, I get the message: "A software update is required to connect to iPad." I run the update (over, and over, and over, and over....) Sometimes it fails, sometimes it doesn't. Even when it doesn't, the device does not show up in iTunes anywhere. Disconnecting and reconnecting the iPad brings up the same message, and the same install. Sometimes the failure message is "can't download the install because of a network problem," yet no network problem ever exists.
So, I have no way to backup this piece of junk (running iOS 14.5.1, not that it matters), and no way to use my new iPad. Any suggestions?
I've restarted. Both devices. Many times. I've signed out of iCloud and back in. There is plenty of space on iCloud (there was before, but I still upped the plan so I have at least enough space to backup the device twice without interfering with any existing data from it in the cloud). Both devices detect the connection. iTunes is 12.9.5.5, but I see no update for that even if that were the problem, which isn't likely, as it's asking for the update for the iPad. iPad is on, unlocked. OS 10.14.6 (updating is not an option, and this should work with the device under these conditions).
iPad Pro, iPadOS 14