macbook pro m1 8gb , purple screen crash, mac restarts itself

Etrecheck

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.

Point # 2 - Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation. The Built-in Security of Big Sur is all that is required.

Firstly, the version of Big Sur is not yet totally up-to-date. There is a Big Sur 11.5.1. Further, does this happen in Safe 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.

I had the same issue once on M1 16GB 1TB, the machine start stuttering while playing audio and video and after a day or two crash. I submit the report to apple so that they can fix in new update.