Yeah, a tankless pulls down power like an EV, and since conversion to heat is 100% efficient (loss in the pipes on the way to your shower notwithstanding) you actually need that power to heat up the water at the speed a tankless sends it through. That's why the gas ones work better, hydrocarbons store a shitload of energy.

Yeah, although electric heat is 100% efficient it takes a lot of energy to heat water quickly. You're better off going with gas for hot water on demand. I imagine the unit price is more, but the install price will probably be lower.

The 3.5 kW heater will have a tank reservoir that will have time to heat up the water when it's not being used. Tankless means it has to be heated instantly.

It takes ~ 4 kJ to heat 1 kg of water for each 1°C. If you want to do that in 1 second, you need 4 kW of heating power.

So if a shower uses, say, 9 litres per minute, i.e. 0.15 litres per second, heating that water from 10°C (typical cold water temperature) to 40°C (comfortable shower temperature) is:

4 • 0.15 • 30 = 18 kW

Anything less heats less water per second, or to a lower temperature.

Like this 5.1 l/min unit at 9.5 kW will be able to heat that flowrate ~28°C above its inlet temperature.

For the shower you'll want the 18 kW, otherwise you'd have to shower with a tiny stream of water. What you have is meant for washing your hands (tiny one under the sink).

Yup. That's why people use smaller heating elements and slowly heat up lots of water in an insulated tank instead. Just the difference in the cost of wire you need to run is massive.