I think what "has not been retouched or post-processed in any way" is supposed to convey is that no work is needed by the user of the camera app to get pictures of this quality. There's lots of in-camera processing of course. That's always been the case for digital cameras: sensors don't produce jpeg files.
The problem is that the definition used to match the capabilities. The capabilities changed. Should the definition? If I say I haven't retouched or post-processed a picture of myself, you used to be able to assume it hasn't been airbrushed or edited to make me look fitter. In fact, that used to be how you'd say it. Linguistically, it's extra weird when you're announcing a new auto-retouching and auto-post-processing feature.
Exactly. And heavy post-processing is necessary for even very simple things because a camera's sensors don't match the output picture all that well. See for example https://en.wikipedia.org/wiki/Bayer_filter#Demosaicing. The postprocessing has moved up the semantic stack and now cameras do things like face detection and smoothing, but there's always been some amount of postprocessing in digital photography.
What people are trying to say is that if this is your definition of post processing then there doesn't exist any digital camera system that produces photos without post processing. Indeed such a camera cannot exist.
I know, I work in digital image processing, and I'm an amateur astrophotographer. Demosaicing is not on the same level as star registration, stacking (posibly HDR processing in the middle), plus some more AI driven "magic" in between.
That's what I'm referring to: for the shown image "without post-processing" the phone has performed a lot more actions after demosaicing, that's why i say it was heaviliy processed.