This copy of the Install macOS Monterey.app application is damaged.

Hmm. Just to be absolutely certain there is no "hidden" installer, try entering the following command in the Terminal app:

• lsof | grep <the installer's filename>

If the result doesn't show any, I'm afraid that I'm out of ideas on why this is happening. The only other things I can suggest would be:

• Boot up in Safe Mode, and try downloading it again OR
• Create a new user account. Log out of your existing account, and then, log in with the new account. Then try downloading.

The support article you arrived here from should provide you with the steps to upgrade to macOS Monterey. Did you follow them and you still get these "damaged" files?

If so, it is most likely that the App Store is still detecting that you have an existing copy of the installer in your Applications folder. If you have, and already deleted it, make sure that you empty the Trash. Also, double-check to see that an existing installer is not present anywhere else on your Mac ... like the /Library/Updates folder.

There are factors:

1 - Like poor Wifi connection

2 - Slow wifi connection

3 - Too many other people downloading at the same time and Apple Severs are overloaded

4 - Software on the computer interfering with the download process including AntiVirus Software

5 - Running behind a VPN which may increase Packet losses and possibly even a corrupted Download

6 - If via wifi too many Other devices using the wifi at the same time reducing the Bandwidth to your computer. 

7 - Best Results are via Ethernet Cable to Router

Where exactly are you downloading the macOS Monterey installer from? Is your goal to upgrade from another version of macOS, or to perform a "clean" installation?

Honestly, I don't know. However, moving it back may be worth a try. Good luck!