What is the update this will install? I'm currently at Catalina 1.15.7

Shorter version of the above: it’s an update to Finder to allow it to communicate with the iPhone. Nothing else changes.

According to If you see "Software update is required to connect to your iOS device" on your iPhone, iPad, or iPod touch - Apple Support:

"When you connect your iPhone, iPad, or iPod touch to a Mac with macOS 10.11 or later, you might need to update the software on your Mac in order for it to recognize your iOS device." 

Only the software which allows your computer to communicate with your iPad will be updated.

Greetings, and welcome to Apple Support Communities HelpNeededxx,

We can see that you're unable to sync your newly updated iPad with your Mac mini.

This might help: If you see an error in Finder or iTunes on your computer You'd want to follow the directions, including seeing if there are any updates to your Mac. You can find this in the App Store on your Mac.

If you'd rather not update your Mac, you can also back up your iPad using iCloud. Here's how: How to back up your iPhone, iPad, and iPod touch

We hope this helps!

thank you for a simple answer to a complex problem. How many of us have been aghast to discover some trick of apple has us updated to a new OS we neither want or need?

You are welcome.