Hello guys. I have been bothered by this issue for many days since I upgraded from my iPhone 7 to a new iPhone 13 Pro in October. So I have read the comments here, and want to also add some based on what I have seen in China.
In China, so many people are complaining about this camera quality issue, mainly about how over sharpened and over exposed the photos are and how we can't even change it in the first place. So many have complained on social media how the iPhone 12/13 camera makes their pets and selfies "old and ugly" (hair looks greasy, etc.). On top of that major issue, sometimes when you tap on 3x, the camera still uses a digital crop of 1x, which is confusing and unnecessary and produces the "watercolor" effect. I believe users should be able to choose the lens they want in any circumstances, rather than being forced to use another lens.
What's funny is that (second-hand) iPhone XS/XR are sold at a higher market price now because of their better cameras. Many people are saying the iPhone X series can take the best selfies. My old iPhone 7 even takes more natural pictures than my 13 Pro.
Also, due to this issue, people have found some workarounds. Here are what I have seen.
1. Take live photos and choose another frame as the cover, because only the original cover is overprocessed. Personally, I don't like taking live photos, so it's not my favorite choice.
2. Use burst mode by holding the “Shutter” button and drag it to the left, which would produce photos without the overprocessing.
3. Use third party apps, as so many here have already mentioned. Some Chinese developers have also made similar apps. But the subscription is a bit expensive.
4. Take ProRaw photos, but the downside is the photos are too large in size.
So far, I have tried all those methods, and I think ProRaw makes the best results but are too large. So I often use burst mode to bypass the baked in overprocessing. But I really hope Apple will be aware of this huge issue and correct it in future updates! Never would I have ever imagined a new model would take worse photos than much older models.