Yes, it does. I haven't tried it as a do not have the cable for it, but the user interface for discharge is there and the manual also talks about this feature.
It's probably not ideal for running a full house (as it would require some other electronics and installations), but a couple of appliances should work.
There are several types of bidirectional EV charging, the one most cars has is about a 1kW fused connection called "Vehicle to Load (V2L)" but the one you are discussing is what they call "Vehicle to Grid (V2G)" and in those cars it supports the full input and output of the vehicle inverter.
Those batteries must be connected to the internet to work, and the company could disable them anytime. Same for most of the inverters. I’m just hoping they don’t pull some nonsense like we have seen with other “cloud” devices. In that sense, I trust Tesla as much as BYD, and that is not at all.
You can buy a BYD HVM 22.1 kWh for 6000 euros now (£5200) vs powerwall 2 13.5kwh for 7000 euros.