Bluetooth is a 3000+ pages spec that's a mess and will likely always remain a mess. Maybe it's time for something better?
I would never trust any wireless keyboard or mouse on any even marginally important computer. Bluetooth security is a broken mess, and taken together with the mess most bluetooth functionality is (e.g. perpetually broken, laggy, stuttering, forgetful, lofi audio profiles) bluetooth needs to die asap.
Bluetooth 4.0 (4.1, 4.2, 5.0, 5.1) are almost exclusively the artist formerly known as Bluetooth LE. LE is a totally different standard than classic Bluetooth, and was developed by Nokia ("Wibree") and dropped on the desk of the SIG with a big thud. Nokia told the SIG this was Bluetooth now, and they adopted it as "LE" and it forms the core of all version of Bluetooth 4.0 and later.
4.0 and later specs include "LE", "Classic" and "High-Speed". It's very unlikely developers are building for Classic mode anymore, that protocol is an utter nightmare. I don't know anyone building High-Speed devices.
I'd be surprised if a new keyboard opted for anything other than LE. That's just the kind of embedded system it was designed for.
Perhaps you can clarify whether I was barking up the wrong tree in my original comment; My understanding is that keyboards, HID devices in general, are usually using something like "Classic mode" or perhaps even actual classic Bluetooth (particularly cheaper/older hardware)
The security keys like the are using the "modern" type, which is a different "spec". I don't know if it's using something like like (G)ATT, but it's not the same spec/tech?
Older devices almost certainly use a Classic Bluetooth HID profile, but newer devices like the Apple Magic Keyboard are LE HOGP devices. It uses much less energy so IMO a battery-powered HID device would be pretty nutty to implement using Classic Bluetooth in this day and age.
Interestingly there's no concept of "pairing" in LE devices, just "bonding" (where previously derived keys are persisted and re-used as an optimization). All LE peripherals operate in promiscuous mode by default and vendors have to implement their own pairing system -- or piggyback off bonding.
 Warning PDF link: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&c...