Hi sidonie96,
Thanks for the detailed description. Given that you bought the new MacBook Air in September, I'm guessing it uses an Intel processor, and has the Apple T2 Security Chip.
I'd recommend running a hardware test on your Mac to ensure that the issue is only with software. To do this, please see this article: Use Apple Diagnostics to test your Mac - Apple Support. If no issues are found, it should show the success code ADP000. If you see a different code, Apple explains what they mean here: Apple Diagnostics reference codes - Apple Support
If no hardware issues are found, I'd recommend starting up in Safe Mode. This prohibits any third-party apps from running automatically at startup, and helps investigate app issues. If no issues occur in Safe Mode, but do occur in normal mode, the issue is likely related to a third-party app that runs at startup time.
If the issue continues to occur in Safe Mode, I'd recommend doing the following, and testing whether the issue persists after each step:
- Reset NVRAM: Reset NVRAM or PRAM on your Mac - Apple Support
- Reset the SMC: How to reset the SMC of your Mac - Apple Support
- Reinstall macOS (DO NOT ERASE YOUR DISK): How to reinstall macOS - Apple Support