[Fulltiming]

You either have an issue inside the transfer switch since the case should not have any electric charge on it so touching a braided stainless hose should not have caused an issue OR the braided hose was in contact with current at some other point also.

Looking at the photo, I don't see any visible damage inside the transfer switch. An electric arch between the case and the hose should have caused a breaker to at least partially trip in the main 120 Volt AC breaker panel in your bedroom. I would shut off all power, including the inverter and charger then carefully examine the inside of the manual transfer switch to insure that all connections are tight and there is no sign of a short inside the transfer switch. You have the main relays that switch power from shorepower to generator and on my 1992 attached to the side of them are smaller clear relays that are designed to prevent both circuits from being energized at the same time but I don't see them in your photo. Pay close attention to any chaffing of the electric wires coming through the rear of the box. If the insulationh as rubbed off there or if the clamp fitting on the back was tightened so much that it cracked the insulation, you could get a flow of current to the transfer box itself which would be a very dangerous situation.