M3 purple screen crashing

Try and boot the mac in the safe mode to see if the issues persist.

If the issues don’t persist in the safe mode they’re caused by An external piece of software, you might want to evaluate the software installed to your mac

Start up your Mac with Apple silicon in safe mode

1. On your Mac, choose Apple menu  > Shut Down.
2. Wait for your Mac to shut down completely. A Mac is completely shut down when the screen is black and any lights (including in the Touch Bar) are off.
3. Press and hold the power button on your Mac until “Loading startup options” appears.
4. Select a volume.
5. Press and hold the Shift key, then click Continue in Safe Mode.
6. The computer restarts automatically. When the login window appears, you should see “Safe Boot” in the menu bar.

If the issues do persist in the safe mode I suggest hardware error. As your mac is only a month old, take it back to where you’ve bought it to have it looked after under warranty