Latest version of macOS Monterey 12.7.6 not available on App Store

Within that linked article is a link to another article that has links to various macOS installers. See if the Monterey link in that article will give you the 12.7.1 installer. Here is a direct link to the Apple article which has links to various versions of macOS:

How to download and install macOS - Apple Support

If that still does not give you the proper installer, then try using the Terminal with the following commands....the first will check to see which installers are available for your computer while the second is the command to download a specific version of macOS installer....you need to use one of the valid version numbers from the previous command:

softwareupdate  --list-full-installers

softwareupdate  -d  --fetch-full-installer  --full-installer-version  <version-number>

For macOS 12.7.1, the last command would be:

softwareupdate  -d  --fetch-full-installer  --full-installer-version  12.7.1

If none of this works, then try rebooting the computer. I know when Sequoia was first released none of my computers would show the most recent versions or even download them. It was a month later when my laptops finally were able to list all of the available versions & allow a download using the command line. Sometimes these Macs just get into a state where they won't properly see the update....or it could be an Apple issue (or both).