Monterey upgrade

Try booting to Recovery and use the Disk Utility in Recovery and do First Aid on the startup disk. That will check is the disk is ok. The error message "Storage system verify or repair failed." may mean a bad disk and thus the installer prevents the Monterey install. Use the Recovery instruction included here:

How to reinstall macOS - Apple Support

YOu can't really perform First Aid on the startup drive since the drive has to be unmounted to do First Aid.

You may have to use a wired keyboard since sometimes it does not work with a wireless keyboard.

Also some other uses here reported that their 3TB fusion drives in their iMac's failed and that prevented upgrading to Monterey. Maybe yours is failing

Do you have the original Apple SSD installed internally and is it working? Monterey upgrade includes a firmware update to the Mac and it checks if you have an Apple SSD installed. It fails to install if not.

There have been some people - not you as it turns out - who have changed the Internal Drive from the original drive installed by Apple to a Third Party Replacement drive.

Those same people, when attempting to upgrade to Monterey, were greeted with a error message saying Monterey could not be installed on this Drive. That was although the computer Qualified for the Monterey upgrade.

Hope this clears up the head scratching .

The reason to ask about the File Format of the drive - some people running Mojave 10.14 have not allowed Mojave to convert the filing system from the Old HFS Journaled / GUID to the newer APFS / GUID used in High Sierra, Mojave, Catalina, Big Sur and now Monterey.

Had this been it case for this computer - it may have been a factor when installing or attempting to install Monterey

As previous poster mentioned regarding After Market internal drive issue.

Added - what file format was the Mojave drive ?? HFS or APFS - should be APFS for better results.