Goth expert here. A lot of first-wave goth bands (Bauhaus, Siouxsie, etc.) are undeniably jazz influenced, do your research. And of course goths are allowed to like non-goth music, but jazz is considered one of the seven main genres of what constitutes "goth music" as a whole.
Post-punk, death rock, goth rock, darkwave, ethereal, industrial, and jazz.