An internet connection is required to install macOS. This error keeps popping up when I try to reinstall macOS

that message is self explanatory. so I need to ask, are you attempting the download over wi-fi? when possible, you should perform macOS downloads with a wired ethernet connection. if this is not possible, (mac has no ethernet port) you should move the mac as close as possible to the router, and temporarily remove your other devices from the wi-fi. you need the most bandwidth going to the mac as you can get while downloading a macOS. I would trash the current macOS installer (if there is one) and start over.

look in your "applications" folder for a "install monterey app" if there is one, drag it to the trash and empty the trash before trying the download again. if there isn't one, there's nothing to delete. you can proceed with the download.

this appears as though it's an M1 Mac. if it is, you need help from someone who knows the subtle differences with this operation on an M1 Mac. worry not, there's a lot of them in these pages. :)

you're welcome.