Sorry to hear about the trouble you are facing. I would suggest you try resizing the Save As dialog box and let us know if you are able to save or not. Please check the following GIF for reference. Let us know how it goes. I hope it helps!
We are glad to inform you that the save button greyed out/ unclickable issue has been addressed. We worked with Apple and addressed this issue with the latest macOS update, v12.3.1, released last week. I would request you to update and let us know if the issue still persists.