it will not find the monterey update on my late 2015 iMac running Big Sur

Have you searched Monterey in the App Store?

Once download is complete it'll ask do you want to proceed. Sorry about the big pic, I see too many that are hard to read so I just attached the raw capture.

If you still can't find Monterey in the App Store, you can do the internet recovery boot to update the Mac.

Option-Command-R: Start up from macOS Recovery over the internet. Use this key combination to reinstall macOS and upgrade to the latest version of macOS that’s compatible with your Mac.

But before you update the Mac, it is a good idea to create a backup first to avoid data loss

These articles have the same reminder to create a backup first

How to upgrade to macOS Monterey - Apple Support

Update macOS on Mac - Apple Support

Hope that helps!