Most likely it's either an issue within the user account or the software. You can restart the Mac in safe mode, as this helps to clear out the caches in the operating system. Once you go in safe mode under your user account, simply restart the Mac again to exit out of safe mode.
Then, download Chrome on the Google website and follow the suggested steps again to make it the default web browser.
Here's the steps on safe mode:
Start up your Mac with Apple silicon in safe mode
- On your Mac, choose Apple menu
> Shut Down. - 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.
- Press and hold the power button on your Mac until “Loading startup options” appears.
- Select a volume.
- Press and hold the Shift key, then click Continue in Safe Mode.
- The computer restarts automatically. When the login window appears, you should see “Safe Boot” in the menu bar.
If that doesn't help, you can reinstall a fresh brand new copy of macOS Sonoma 14.5 by going into macOS Recovery. This will not delete your data, but it's always recommended to ensure you have a backup on an external hard drive just in case. To reinstall macOS Sonoma 14.5, you can follow this article on Apple's website: How to reinstall macOS - Apple Support
Just make sure that you follow the section specific to Apple Silicon, as that's the processor you have for your MacBook Air M3.
Best of luck!