Do as pervious suggested.
Out of interest, what is the Output of the Terminal command below ?
softwareupdate --list-full-installers
Does Monterey 12.5 appear - Yes ? in Terminal as per below
softwareupdate --fetch-full-installer --full-installer-version 12.5
The Full Version will download ( about 12.24 GB in size ) and place a new application in Applications folder called ' Install Monterey "
It will not auto launch
You will need to launch it like another application and in this case follow the prompts including Manually Inputing the Computer Password - normal