How many wattage is your bathroom electric heater actually?
I doubt anything drawing 8kW is going to have a plug, but if it did it would be a very large plug like an electric stove or clothes dryer.  That said, these heaters typically have multiple heating elements.  It's possible that not all the elements are turning on based on the water flow or that some of the elements are bad.

From what I could find on that product, it seems to be sold in Malaysia.  If it was sold in the US, it would have a label or plate that listed the electrical requirements on the back or on the inside of the wiring cover.  I'm not sure if that's true in your part of the world, but I would look for such a label rather than relying on information from the internet.  For simple devices like a heater, those electrical requirement labels tend to be accurate.

Edit based on internals:

The large copper "tank" on the right is the heating unit, and there seems to be only one.  The label indicates that it could use up to 6000 watts at 240v. The label in the bottom right also seems to indicate 6kW is required.  To me, that indicates that the wiring going to the device should be rated to handle 6kW (25 Amps).  If the plug it's going to is protected by a 15A breaker, then you wouldn't have to worry about melting wire - you would just trip the breaker if too much power was used.

The two tubes at the bottom would be the water inlet and outlet.  There might be a flow sensor on the inlet side behind the bracket.  The wires connected to the bottom of the heating unit look to be a high-temperature cutoff switch that's common on heating appliances - or even just a temperature sensor.

The copper stubs at the top of the tank are the ends of the heating elements.  It's hard to tell, but it looks like there might be 4 stubs which would be the two ends of two heating elements.  Because there are so many wires going to the top, there could be some multi-stage electronically controlled magic going on that only uses the current needed to heat the water to a set temperature.  Incoming water temp and flow rate could determine the amount of power needed.

The black box with the two red wires on top of the heating element might be some type of high-pressure cutoff.  I don't think you would need red, thick wires for a temperature or flow sensor.