When taking a bath with a water heater, just turn off the switch on the water heater or turn off the power switch. Will it be dangerous if the power supply is not stopped?

Downstairs, that's right. Generally, water heaters have a bottom line, so don't worry about danger, but as you know, everything is not 100%. I suggest you unplug it, because it won't delay your use anyway. It's best to cover the power socket with something now, otherwise there is a danger of leakage when the steam is too strong in the shower.