Hi there,
From what we can tell, your MacBook Air is performing slowly when using Photoshop, and you're unable to save projects due to an error that appears. We're glad you've joined us in Apple Support Communities and we can provide some guidance.
To start, for this specific behavior with Photoshop not responding as expected, work through the suggestions in this support article:
If an app on your Mac stops responding, closes unexpectedly, or won’t open
To address any slow performance issues on your MacBook Air, even while using Photoshop, follow the steps here:
If your Mac runs slowly
Also, check out this link from Adobe with compatibility information and details about known issues in macOS Big Sur:
Photoshop, Apple Silicon, and Big Sur | macOS 11
Cheers.