Follow the advise @Matti Haveri has suggested.
As late resort, also from Safe Mode - In Terminal " softwareupdate -l " without quotation marks.
The same procedure re-quotation marks this command " softwareupdate --fetch-full-installer --full-installer-version 12.0.1 ".
This should download the Full Installer and place a new Application called " Install Monterey " in the Applications folder.
If successful - it will not launch but just sit there.
Do the TM Backup and if wanted, copy the installer to good external drive for future purposes like a bootable installer.
Run the Installer at this point.