MBA Freezes when using Projector - it's a new thing

Try and see if this is happening in the safe mode. If it is not happening in the safe mode it is most likely 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.

Start up your Intel-based Mac in safe mode

1. Turn on or restart your Mac, then immediately press and hold the Shift key until you see the login window.
2. Log in to your Mac.
3. You might be asked to log in again.
4. On either the first or second login window, you should see “Safe Boot” in the menu bar.

If the issue is persisting in the safe mode you might want to give this as feedback to apple, do that via this form, so they can look in to it

Product Feedback - Apple