Yeah this is super helpful as I'm thinking through my system.
We have only one Powerwall and so none of the 240v appliances (A/C, dryer, oven, level 2 EV charger) are backed up. Our installer made this happen by repurposing our electrical panel as the backed up loads panel and moved those four 240v circuits to a panel that sits before the TEG - during a grid outage that panel and the circuits are de-energized. This also means there are no double pole breakers in the backup panel since they're all only 120v circuits.
I also have a 1200w inverter harness setup for my Volt. In the case of a prolonged outage when the sun is not sufficient to run the house I intend on running extension cords to some reachable appliances such as the garage freezer and kitchen fridge to shed that load from the Powerwall, in effect doing exactly what your MTS does
@Flick75.
What I'm wondering now is if I could wire in an MTS between my backup panel and the TEG for my Volt harness. I'd have to be extra careful not to overload the inverter but could easily put a 10a or 15a breaker or fuse between. If there's a prolonged outage I'd flip the MTS and plug the Volt in to the generator input. That way I could power up to 1200w of house loads off of the car. Biggest question I have is that the inverter is single phase 120v and the backup panel is 240v split phase. I don't think its actually a problem but I am not an electrician