Any chance the HDMI cable is just kinda snooty about when it decides to work? Can you try with one from a different device?
Unhelpful tip most likely, since it apparantly does work ~sometimes~ and with HDMI you would kinda expect it to either work completely or not at all. Getting image but no sound seems unusual for a combined signal... That said, the HDMI cable that came with my Wii U is kinda uppity about working with my laptop, and requires some feathering, so maybe Ninty just ships crap cables?
Hope it auto-fixes for you permanently. Idk how saves are handled on Switch, so maybe finish Mania and Zelda first before sending it in... Ugh.