Monterey still won't install...

 If rebooting your Mac doesn’t fix things, see if the problem still happens in Safe mode (hold the shift key down at startup). It can take much longer to safe boot (10 min) so be patient.

How to use safe mode on your Mac - Apple Support 

Safe mode forces the OS to clear certain caches and logs and do other miscellaneous housekeeping. It's non-destructive to user data so is safe to do. Very often certain weird software behavior is corrected by simply logging in this way as a troubleshooting method. When you're in safe boot, the machine will not be at its best performance, especially with graphics, but that's expected.

Try upgrading the computer while you are booted in safe mode.

Does the problem still persist?

Exit safe mode by restarting your Mac normally and re-evaluate the issue again.

If the problem is still unresolved, please return here and post a reply and we’ll see what else we can come up with for help.

If restarting in the Safe Mode doesn't work, I have to ask you if you have been using Wi-Fi for the downloads? That could b the problem. Sometimes it works fine, but many times Wi-Fi is simply too slow for these very large files and they get corrupted during the download. Instead, connect to your router with an Ethernet cable for the download. If you have to, then temporarily move the computer. I hope this helps.