I recall some years ago, someone submitted a greeting for Conlangery that was a bunch of insect sounds. According to the conlanger it is meaningful, though I don’t vet greetings too thoroughly.
Also, in my earliest conlang, Yeltax, there is a harmonic tone, with two simultaneous pitches. It’s impossible for humans to produce in normal speech, as the aliens who speak Yeltax have a syrinx, which makes two base frequencies possible. (Note: I made that before I learned any phonetics, and now I think I’d want to think about the acoustics here to distinguish this from the harmonics we use for vowels.)
In general, though, most conlangers don’t make up too many sounds. Many of the gaps in the IPA chart are physically impossible, and it’s questionable that we’ve missed a major articulator. I think most of the true inventions will be for non-human languages.
Leaving behind sound, though, it could be said that Rikchik has a robust alien phonetics that was invented from scratch. Since the aliens have many tentacles for signing, and a very non humanoid appearance, their signs can’t be related to any of the features of signs in human sign languages. Once again, invented phonetics is probably going to be for aliens.