I don’t think it will be fixed soon. iPhone 12 did same thing. The sky in the photo is bluer than reality. It seems like when iOS recognize this is sky, it will make it bluer. This is a problem when sky is grey, iOS still add blue color to photo. The photos just not looks normal at all. On iPhone 12, I can turn off scene detection and smart HDR. These options disappears since iPhone 13. You can try Proraw or live photo. It seems like Live Photo, the moving part has less postprocess.

Before iOS 13, the default option Fetch automatically works fine. I can get notification from mail and Gmail at same time. Since iOS 13, it only works when you are charging your iPhone. So you have to use Gmail for notification.