The pump used for the gas stove is sensitive to "running dry" which can lead to damage to the rotor/impeller/sliding surfaces. The pump will then make noise and not work optimally. The video shows a pump that is noisy and does not produce any water flow.
The pump can be checked by opening the end and removing the impeller and rotor.
The pictures here show how the rotor and impeller should look.
Damaged parts are shown here
Water flow is obstructed
Noise from the pump is typical when it does not receive enough water flow and then the electronics/control for the gas heater does not work either.
Normally connections should not limit the flow but if the hose is bent as seen here in the video it can cause the pump to not get enough water and make noise.
The noise here is also due to too little water flow.
Similar problems also arise if the filter before the pump is not kept clean. The filter is only designed to remove minor impurities to protect the pump and stove. Clean the filter after each use of the bath. Use separate filtration for good water hygiene.