If the running water noise continues once the tank is filled you may want to call a professional plumber to investigate the situation for you.
Tankless water heater noisy pipes.
The sensor controls the amount of gas sent to the unit.
If you hear a weird groaning sound from the pipes or the tankless hot water heater when you flush the toilet that could be the culprit.
Inside a condensing tankless water heater the combustion process superheats the water that enters your shower sink etc.
Even though a toilet only uses cold water i have seen some toilets do this.
Generally speaking there is a lower chance of hearing strange noises with a tankless water heater vs tank model.
Another standard issue that causes loud noises in tankless water heaters is a dirty flow sensor.
Although keep in mind that it is normal to hear water entering the tank when hot water is being drawn.
Other sources of noise include blocked or inadequate ventilation or a defective or improperly set pressure valve.
If your water heater is making noise like water is running you probably have a leak or a broken pipe.
Another common problem that can create noise in tankless water heaters is a dirty flow sensor which controls how much gas is sent to the unit.
Or you can try to run down the leak yourself by checking the following.
A blocked or improper ventilation and even a defective or wrongfully set pressure valve can also make your tankless water heater loud.
Water vapor is a byproduct of combustion although in this case the vapor contains elements such as methane nitrogen and oxygen.