Strangely, I can't find any references to anyone else having this problem. This question is close, but that OP is using a work phone with security profiles that prevent any bluetooth settings changes. My problem is that one—only one—bluetooth device is missing the (i) button, which means I can't forget that device. An unforgettable bluetooth pairing! Has anyone seen anything like this before?
The reason I care, of course, is because I'm having very bad connectivity issues with that one device. The only troubleshooting instructions are to forget and then pair again, but I can't forget!