iPadOS 16.1 won't install on compatible iPad

iPadOS16.1 is available for these models of iPad:

• iPad Pro (all models)
• iPad Air (3rd generation and later)
• iPad (5th generation and later)
• iPad mini (5th generation and later)

If your iPad is capable of being updated to a more recent version of iOS/iPadOS than is currently installed, these support pages outline both the available methods by which the update can be performed - and troubleshooting should you experience difficulties:

Update your iPhone, iPad or iPod touch – Apple Support

If you can't update or restore your iPhone, iPad or iPod touch – Apple Support

If your iPhone, iPad or iPod touch won’t update - Apple Support

iOS update and restore errors – Apple Support

Be aware that while an iPad may be capable of update, it may be too far behind the current version to be updated directly from iPad settings. In such circumstances you will likely need to use a computer to perform the update. You will need access to either a PC (with iTunes installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of MacOS). Ensure that your installed version of iTunes has been updated to the most recent version; the essential device drivers are included.

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Update software on iPhone, iPad or iPod touch in iTunes on PC - Apple Support

If you have a beta profile installed, ensure this has been removed from your iPad - as, otherwise, installation of production software updates may be inhibited. This support page provides the necessary information to remove the beta from your iPad:

How to uninstall iOS beta software - Apple Support

You should note that for your iPad to install an available update, its battery must be charged to at least 50% capacity - and/or be connected to its Power Adapter. Similarly, the iPad can only be updated over a standard WiFi connection - or be updated by a PC or Mac using iTunes or Finder - over a USB connection.

Have you previously used a beta version of iOS?

If so, remove the beta profile, restart the device, and check again for the update.

How to uninstall iOS or iPadOS beta software - Apple Support

My iPad Pro says I can upgrade to 16.1, but when I provide all my credentials it thinks for a moment and tell me it'll need to unload some apps and will load them back on. I can either agree or cancel. Cancel just aborts the upgrade process. Agreeing makes it go and think, but then it either aborts the update on its own or it gives me the same prompt about offloading apps.

Not sure how to get past this. My next idea is to reboot my iPad Pro and see if I get a different result. I never had a beta version installed. I believe my iPad Pro should have plenty of space free as well. So I'm a little perplexed.

Do a  force restart your device.

then offload some content and then try updating again.

You are quite welcome, and thank you for the feedback.