The term is a phonological one rather than a phonetic one, though given common assumptions about phonological properties, that implies (falsely IMO, but that's another matter) that it is a phonetic property, because phonological properties are widely thought to be really phonetic in nature. I don't think I have ever seen a phonetic paper (i.e. something published in JASA, JoP, Phonetica) ever claim to quantify "sonority", but it is possible that some phonetic paper has referred casually to the phonological account (e.g. "we would need to look at segments of high sonority"). There are phonological accounts which attempt to relate "sonority" to a physical property, namely properties of the vocal tract which result in minimal signal damping. See Hume & Odden ("Reconsidering [consonantal]") for an account in terms of "impedance", i.e. those factors in the vocal tract configuration that increase resistance to airflow. This relates to amplitude of the signal, but factors out differences in the source which make amplitude an unsatisfactory measure of whatever "sonority" is about. This is, however, a speculative account of the concept "sonority" (the inverse of "impedance"), posited simply to show that the feature [consonantal] is not necessary in order to compute that relation where V > y > l > m > p.
To the extent that phonological theorists posit phonological devices that derive the scale V > y > l > m > p, you can say that it is a phonological concept. There is a substantial debate over whether sonority is a legitimate concept, as opposed to being epiphenomenal. The latter account says that grammatical machinery doesn't need "sonority", instead the observed patterns ([.prV] but not *[.rpV]; [Vrp.] but not *[Vpr.]) are explained perceptually – the "marked" sequences are harder to perceive than the "unmarked" ones.
So in that account, the response is simply "Sonority? What's that?". Among theorists who believe that sonority is a primitive property of segments, it seems that the prevailing oipnion is that "sonority" is a scalar phonological property, which can have some number of values, around 6 or 7.
The question about phones and phonemes is based on a premise that was rejected decades ago, namely that the (allo)phone / phoneme distinction entails different grammatical mechanisms. On the other hand, the attempt to say that the phonetic causal mechanism is part of the phonological computation results in a causality paradox (you have to access the actual physical outcome so that you can compute what the phonological output is, which then results in the actual physical outcome). Hale & Reiss The phonological enterprise discuss the phonological substance abuse problem at length. Most often, phonologists who believe in sonority consider sonority to be a grammatically arbitrary property whose existence can be rationalized by reference to a phonetic explanation.
It's also not clear whether sonority is a "feature" of any sort. "Feature" has a specific meaning in phonology ("syllable" is not a feature), and sonority isn't generally treated as a feature. I don't think many phoneticians believe in "phonetic features". However, you might have intended "property", a fairly non-commital term.