There is that one Logitech keyboard that does this. It has a selector dial on the left where you pick which one of 3 possible devices to connect it to.
There is still the design problem there however. You kind of have to guess which one 1, 2, or 3 is. And you need the recipient device to actually be on and maintain the connection when you make the switch. So it's not just 1 UI interaction. Depending on your situation, there can be at least 3 and they're spread across multiple devices.
Ideally we'd have a standardized overlay or display on any bluetooth device to indicate its connection status and what it's paired to. But that would be its own headache and would seriously constrain how devices can look or be shaped. How much UI can you really fit on a pair of headphones that are meant to be small?
There is still the design problem there however. You kind of have to guess which one 1, 2, or 3 is. And you need the recipient device to actually be on and maintain the connection when you make the switch. So it's not just 1 UI interaction. Depending on your situation, there can be at least 3 and they're spread across multiple devices.
Ideally we'd have a standardized overlay or display on any bluetooth device to indicate its connection status and what it's paired to. But that would be its own headache and would seriously constrain how devices can look or be shaped. How much UI can you really fit on a pair of headphones that are meant to be small?