trying to update from os high sierra to monterey and getting the error messageThis copy of the Install macOS Monterey application is damaged, and can‘t be used to install macOS.

You are getting the message that the installation file has been damaged because it has been damaged and will not load. Did you download it via Wi-Fi? If so, don't use Wi-Fi. Put the old file into the Trash and empty it. Then do a clean download using a wired Ethernet connection. It should go fine. If necessary, temporarily move the computer to use a wired Ethernet connection. If that is not possible, you may have to do multiple downloads via Wi-Fi to get an uncorrupted one that works.

Also try upgrading in steps vice skipping macOS versions. That is upgrade to Mojave first, then Catalina, then Big Sur and finally to Monterey. SOme users have experienced problems skipping macOS versions, and even fully update one macOS version before going to the next macOS version.

You can get the older upgrades here:

How to get old versions of macOS - Apple Support