Thank you for reaching out. So just to clarify, when you are using the stock gallery app on your S22 Ultra, you are unable to edit or delete new pictures as when you click the 3 dots you just get a loading circle is that correct?
I would recommend trying to delete your photos while your device is in safe mode. If your phone or tablet is misbehaving, it's possible that a third-party app is causing the issue. To figure out what app is acting funny, you can use the Safe mode feature. In Safe mode, your device won't run any third-party apps. Give this link a try: https://www.samsung.com/us/support/answer/ANS00062983/
Did you restore your device from back up after factory resetting it? If yes, you could have put the software causing these symptoms back on your device.