High CPU usage on M1

Ok - to explain what Safe Mode did. It does several things and one of them is Eliminates ALL Third Party Software, extensions and Fonts from loading.

Since your issue is not presented in Safe Mode two possible things come into play. Third Party software installed and interfering with the normal operation of the OS and / or an issue in the Admin Account of the computer.

To narrow the source of this issue - suggest making another User Account only for Testing purposes - it can be removed afterwards. If doing so, log out of the Normal User Account and into the testing account and Test if Messages is presenting the Original Issue ?? If after testing and does not present the original issue - the real issue is in the Original User Account.

Should the same issue happen in the testing account - then the Third Party Software installed is the real issue. To fine tune that would >>>> Suggest downloading the Application Etrecheck directly from a Trusted Developer and well Respected ASC Contributor. The application is free or paid from added features. Run the application with Full Disc Access ( Security & Privacy - Full Disc Access ). It will take a Snap Shot -  both the hardware and software. The Report will Not Reveal Any Personal Information. Post back the Full Report - copy and paste - using the Additional Text Icon ( 3rd Icon to last )

We can have a look at the report for possible issues and may have possible suggestions to resolve the issues.

Any Third Party Applications that will interfere with the normal operation of the OS, alter, modify, remove or delete or attempt to do so is an invitation for disaster and may require a Reinstallation of the OS.

As per below restart in Safe mode. Does the same issue present in this mode ??

Start up a Mac with Apple silicon in safe mode

1. On your Mac, choose Apple menu  > Shut Down.
2. After your Mac shuts down, wait 10 seconds.
3. Press and hold the power button on your Mac until the startup options window appears showing available startup disks and Options.
4. Select a startup disk.
5. Press and hold the Shift key, click Continue in Safe Mode, then release the Shift key.

Is this a New Issue - if so what changes have occurred ??

Is this an Old Issue - if so what actions have been taken to resolve the issue ??