Tesla brakes are conventional. Yes, the driver has to push harder if the hydraulics fail, same as any car. There's nothing unique to the failure here, normal cars run their boosters off of the power train too (via belts or vacuum usually, also some have 12V pumps and would be subject to exactly this kind failure).

As to whether the booster is run off of the 400V or 12V bus I don't actually know. My guess would be the latter, honestly, since the parts would be more generic. But in any case it probably doesn't matter if the main battery fails as the 12V battery is tiny and would probably not provide enough power to run the hydraulics without the DC/DC converter.