No sure how RAW images from that app compare to what you get with ProRAW
As far as I know, RAW is the unprocessed data read directly from the image sensor. I.e., simply the numerical values of voltage generated by light striking each photo pixel. The only processing done by the phone up to this point is the conversion from analog (voltage) to a number (digital). It does not include the conversion of that data into colorful .jpgs. That is the "secret sauce" unique between all camera/phone makers and once "baked in," is irreversible.
Now RAW file formats, the way those numbers are arranged and stored in a file (like ProRAW), vary from company to company (Canon vs Nikon vs Apple...). I'm not totally sure, but I assume apps like Lightroom get direct access to the camera's raw data pipeline since is worked with older iPhone without ProRAW capability.
UPDATE: Traditional RAW and ProRAW are not exactly the same. Apparently ProRAW does store some extra information over traditional raw that allows Apple to use its signature computational photography features. Apple worked with Adobe to add ProRAW-specific data to the DNG specification. So post capture editing like applying portrait mode effects after the picture is taken is probably not available with the Lightroom generated .dng format. It's possible, but I would highly recommend you research it further to make sure Lightroom or any other app can do that. A non-ProRAW raw format will still provide maximum sharpness and dynamic range data, but you may still have to go with the iPhone 15 Pro to get the full ProRAW editing capabilities either on the phone or with ProRAW capable programs... YMMV
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