The closest thing I can think of hits 3 of your 4 criteria is the ThinkOutside Stowaway Bluetooth Keyboard. The only thing it doesn't do is tether with a USB cable.
ThinkOutside originally created a folding keyboard for the Palm Pilot and then had different versions for different connectors for other PDAs. It was a PITA to upgrade and then have to buy a whole new keyboard, but I did every time there was a change. Eventually, Bluetooth became a thing and they migrated to doing a single keyboard. It's chromed plastic and folds into a nice package. There is also a neoprene case that zips around the keyboard when it's closed.
After I switched to the iPhone in 2007, I tracked one down on eBay and I am happy to report that it works. However, I do have to re-pair the keyboard every time I use it and I don't know why, but when I need it, I'm glad that I have it in my bag. I paid $100 bucks for the one I bought 7 years ago, but there's one
for sale on eBay for $78.26ThinkOutside also made a
smaller version, but I preferred the original. I really liked the ThinkOutside company and I was sorry to see them get acquired by iGO and then later fade away. Their foldable keyboard was very unique for it's time and I used the heck out of them back in the day.
Hope that helps!