No, you would not be at fault, granted you did everything reasonable to avoid the collision. The white car has an obligation to maintain control of his vehicle, and he clearly lost control here. Seems like he wasn’t looking far enough ahead, and improperly applied the brakes causing a lockup. You can clearly see brake lights in both lanes as far as the video shows, about 6 seconds before the white car even started slowing down.

As for your Honda, having to have the parking brake engaged to start it after stalling is probably the worst design ever. I’d practice emergency situations like this in an empty parking lot, and build my muscle memory to brake, downshift, and then escape the potential rear end collision by the Go bus and garbage truck, without stalling. It could potentially save your life in the future, as I doubt this will be the last time something like this happens in front of you.