Looks like a B550 series board which means those two headers on the motherboard would be chassis fan 1 and aio pump. If you look closely on the motherboard it should be labeled near the header (in the pic you can just barely read “ch” on the left side and “aio pump” on the right.) The cable looks like a molex to 3 or 4 pin power adapter which would’ve been used with an older chassis fan with a molex connector. If everything is already hooked up you can remove that adapter.
Edit: you can also look up your specific motherboard model and download the user manual which will give you a detailed layout of all of the headers on the board.
Probably not what you’re looking for, but I’ve been really happy with my JBL 306Ps for the last three years. They sound great and can get way louder than I’ll ever really need. Sometimes I wish I went for the 308s for more low end but like 90% of the time I’m satisfied.
Hope you can get your issue resolved. Audio issues are so incredibly annoying.