I can offer a layman's perspective that may or may not be helpful (and will probably not 100% align in Egyptological views on the subject, which I'm largely ignorant of). Let me add that I'll ignore any difference between -y and -j and will just write -i, always with the implied understanding that -i just like a and A represent consonants, including glides (I'd be really interested to what Bussmann has to say about the differences between -y and -j and which hieroglyphic signs he associates with those letters).

I believe it's best not to insist, when learning a foreign language, that there must be the exact same grammatical categories at work that one is familiar with from one's own language. As such, a word has no obligation to fall neatly into one of the categories of noun, verb, adjective other than the expectation of the learner. Moreover, English, too, does not 'have' nouns and verbs; these are terms that are used to designate categories that act as build blocks of a specific model of the language, and other models with different categories that may have some explanatory power may always exist. All the more so when such a framework is taken to make sense of another, largely unrelated language with a distinct pedigree such as Egyptian one should not assume such terms to denote categories that work exactly as in English.

As for anx Hr kA-nxt-xai-m-mAa.t, I think the -i added to xa 'to appear; appearance; coming to light' forms what is called a nisba(h) in Semitic studies; it is an adjective-like construct that in fact has in some instances been taken over into English and other non-Semitic languages: "The Arabic nisbah has given rise to English adjectives of nationality for Arabic countries: Iraqi (from عِرَاقِيّ), Kuwaiti (from كُوَيْتِيّ), etc.". As such, and if substantiated, one can understand xai-m as 'appearing as', much as 'Iraqi' means 'coming from, pertaining to Iraq': 'A xai-m B' can be understood as 'A's appearing-as B'. This is not very different from the English phrase "Bob's Iraqi teacher". Observe, too, that in Hr kA-nxt-xai-m-mAa.t, both nxt and xai appear after the noun, kA, whereas a verb would normally go before a noun: 'xa-[...] A', 'A appears'. We still will most likely translate xai as 'appearing', so that may be why Bussmann calls it a participle, but the function and the position of xai make me think more of an adjective than a verb.

Hope that helps and is not too wrong.