Wow that is a lot of responses, thank you. This is clearly a lively forum! Sorry for not coming back sooner myself.
So the saw I have at the moment is the Makita UC4051A, which is a 2000 W mains-powered saw with a 16" bar. It's advertised in the Makita brochure as having an inertia brake but not on their website... so I asked their customer services and they said the brake was "manual only". So clearly Makita are confused about their own product even.
I can confirm that this saw has the physical metal band that tightens around a drum upon engaging the manual brake using the front hand guard (so I believe similar to a petrol saw in that sense). Perhaps I need to be more "violent" in my nose-drop test, as has been suggested. I was already being considerably more violent than the man in the video though! The front hand guard itself doesn't seem to be weighted, so I presume there would be some internal weights to capture the inertial forces?
Cutting the electric does not stop the saw instantly, although most electric saws seem to have what they call an "electronic brake" or a "rundown brake" as well. This seems to apply a bit of reverse current to bring the chain to a stop when the trigger is released. This does not happen instantly though, it takes about 1 second. I don't think it's meant for kickback protection, just general safety and usability; a lot of modern power tools have this feature.
P.S. The Makita UC4051A looks identical to the Husqvarna 420EL (Husqvarna's only mains-powered chainsaw). I've also contacted Husqvarna and they say the the 420EL has an inertia brake and doing the nose drop test should activate it. I'm tempted to return the Makita and get the Husqvarna but I'm damn as near convinced they are actually the same saw rebranded one way or the other (Husqvarna ignored my question when I asked them if that was the case 😆)