Using third party apps (Lightroom Mobile) does eliminate the cartoonface/oilpainting for me, so clearly one of the issues is caused by Camera app.
I use a mini so no ProRaw for me, but both the DNG as well as the JPG done by LR mobile are free from the exagerated SmartHDR effect done when using native Camera app. (By the way LR DNG result is not a true raw, the compression type in the DNG file is type 7 which corresponds to JPEG)
BUT even without the oilpainting on third party camera app I still get less details than my iPhone 8 in more than half of cases especially on home indoor lighting. I hope to be able to reproduce the experiment using a tripod and upload the samples soon.
I wish I had an 11 or know a friend with 11 to objectively compare same scene at home.
I went to a showroom but it has strong light and it was difficult to tell which one did better sharpness. I airdropped them to my phone and to be honest the 13 is not really standing above the 11 and 12 and the 2020 SE that were displayed in store. Not to mention I could focus a bit closer with the 12 mini and the SE2 and really much closer with 11.