I've run into the same issue and it's not limited to Monterey. The only way I've gotten the installer to work is to drag the installer application from the dmg file into a directory on the Mac. You have to drag the icon from the window in that installer popup, shown in the screenshot in the OP's post, to any of the directories on your machine (I dragged it into my Downloads folder). You then run that copy of the installer application and get all the same security prompts, but it should actually proceed with the installation. I'm guessing it is some security issue that MacOS is getting hung up on with the installer but I've never had the time to actually investigate.
Note: I have yet to see this happen on an AMD Mac. Only Intel based. That said, I've only installed on Mac a handful of times in the last year.