*wireless, not bluetooth*
Just because it doesn't expose bluetooth publicly, doesn't mean it doesn't use it internally. It could still use that software stack, and be hard-coded for only that specific pairing.
And, wireless in general is more problematic than a wire, for things that *absolutely must work*. Your neighbor's poorly shielded microwave could kill your wireless mic or headphones, but a wire doesn't care. Just one of many possibilities.
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Anyway, a common reason for things to suddenly not work in OBS, is that you've left it set to "Default". This is what that does, eventually.
"Default" defers the choice of device to the operating system, which can and will change it for reasons that you might not necessarily notice. But it did switch, and OBS followed that switch, and now OBS is looking at the wrong device.
ALWAYS choose a specific device *in OBS*. NEVER use "Default", unless you have a very specific reason, in which case you probably know what you're doing enough to not have to ask.
Similarly, if there's something you don't use, set it to "Disabled" or delete it. Don't keep stuff around that can only hurt.
"Default" is good to show that a fresh installation works, because it grabs the device that you're most likely to be using at the moment already. Beyond that, it's a liability. Change it.