"Is there any consensus on the security of Bluetooth for keyboards?"
No consensus because security is really big.
So... is there a guard in the guard shack aka an active keyboard / mouse, yes/no just look at a spectrum analyzer for power spectrum in the ISM band BT uses. You can also jam the guards BT devices preventing him from doing anything quite easily. Although once you go active transmitting the game is kinda on.
Some talk about pattern recognition vs time but I've never heard anything "serious" about it. This is the old IBM selectric hack from decades ago where you'd take an audio recording of that classic typewriter and E latency is 7 ms, F is 8 ms, G is 9 ms due to inherent design of the printhead, so you play back the tape and output a near perfect stream of whatever was being typed. Supposedly you can do something like this with BT like the the human key latency between i and n is faster than q and z because no words have a qz. So even if the i and n and q and z are perfectly encrypted such that you'd never mathematically decode them individually, in a sequence representing english text its supposedly easy to decode. Supposedly. I don't think its a practical fear and probably doesn't work for rehearsed muscle memory type passphrases.
Generally you can MITM bluetooth but once you're paired you're OK. So attacker would have to be there when paired. Google for simple secure pairing SSP and I think that needs ver 2.1 or newer (no problemo). Basically if you're not typing in four 0 to pair, then its probably SSP?
Once a BT device is woken up latency isn't so bad but my SIL's mouse / keyboard were famous for about 1 second latency when they fell asleep until they woke up to save power. This would drive me bonkers, your experience may vary.
The tradeoff would be one less cable in exchange for a battery that only fails at the most inopportune time. Eh.