USB Video Camera Audio


First post, first thread, 7 days of OBS and connecting cameras - be kind ...

So, I'm needing a webcam that allows external mic input. I bought a cheapy (80 Euros) on Amazon, connects via USB, video no problem. But doesn't seem to be sending any audio to OBS Studio - audio bar is there but unresponsive - either with internal mic or external mic. I also have an old SONY DVC, connected that via USB video capture from HDMI, that registers USB Audio source and I can use camera mic (internal only) if I wish. So I can find an audio source if there is one.

My question is, is this usual for a webcam or DSLR connected via USB to have no mic input to OBS?
In which case do I have to get a camera with an HDMI out and use a(nother) capture card?

Or .... have I been sold a mare (I can return) and can someone recommend a camera (web cam or cheap vidcam) that allows me to connect an external decent mic that OBS can treat as a separate audio input via USB?
Thanks cyclemat, appreciate your answer. Sony A6300 - nice!
Yes, I have connected a USB mic direct to the PC, but a) was trying to save USB ports and b) wondered if sync offset could be reduced/eliminated by a mic directly attached to a camera. You don't have an amazon ref for your 50 euro one do you? Thanks again.