Why are primary sensory cells considered neurons but muscle cells are not?
The quote from Quora has the correct answer; the distinction between neuronal and non-neuronal is an embryological rather than functional definition. Along those same lines, some of the other receptors you listed are considered sensory epithelia rather than neuronal. The retina is of neuronal origin, but hair cells in the cochlea are often not considered to be neuronal, despite the diagram you provided, nor are Merkel cells. The distinctions between epithelial and nervous tissue are often more difficult to identify because both derive from the same preceding embryonic tissues, whereas muscle is entirely separate.

In the end, these distinctions don't matter much unless you are interested in development or trivia (though I don't mean to discount the importance of development there, I just recommend that you don't worry too much about the distinctions if you are thinking only about final functions).