I'm in the same boat. They've been trying to ship me a wireless as a replacement (I don't want it), and are still claiming they'll eventually send me a wired when they come back in stock.
I tried to get them to just send me the new one, which is cheaper, and they won't.
Dealing with Logitech for a replacement camera is a real headache. I highly recommend just letting them send you a wireless version. Just pop it apart, use your wired base and it behaves 100% the same for HSV.
Zero chance they’ll ever get the “real” wired version back in stock.