arduino with 12.0.1

I am not familiar with that program, but I assume that the reason it's not working is because it needs to be upgraded to work with the new operating system. Check with the vendor to see if they have a compliant upgrade available that you can download. That should resolve your problem.

Apple does not test Arduino connectivity solutions, nor likely do the folks supplying Arduino. Thus, if it doesn't connect now, it may never connect, or may accidentally connect with a future point release of either operating system.

As Apple is not here, there is no way to forecast when this may or may not be fixed. Check with the Arduino source for any expected compatibility with macOS Monterey.

What Arduino version are you running?

I've been using the Arduino beta 2.0.0-11on a M1 Mac mini. I just fired it up and downloaded a sketch to my Arduino Nano as a test and the ID starts up fine., compiles my sketch, and uploads to the board after the upgrade to 12.0.1.

The classic Arduino 1.8.16 also seems to run.

Maybe you should be asking Arduino's customer support or their user forum: Installation and Troubleshooting

It is up to the Arduino platform developers to insure their apps are compatible with the OS it is running on.