What size hot water storage tank with heat pump?

with 300l I would probably keep 100l warm for free most days of the year,

If the tank is well insulated, it only heats up again when something has been used.
My main reason would be an integrated 200l tank in the heat pump, or a standalone 300l, so one less device.
200l is enough for us, the heat pump heats up again if it gets tight.

We also have a 190 L integrated. For the two of us, that’s more than enough. Only when our girls come (both with long hair) do I briefly charge the hot water tank in the morning and evening, about 1 hour is enough. Then everyone has enough hot water. When the ladies are all in the house, it can sometimes get tight (cold).

But 35°C shower temperature and washing hair in 3.5 minutes? Have you all gone to military basic training?

Well, I don’t have 35 degrees now, but a few years ago at a campsite I once had a 5-minute shower token. Anyone who knows Swabians knows what happens next. Since it’s already paid for, it will be used. No matter if you would actually be done showering. It was still a long time until the hot water was gone...

Campsite is one thing, but at home you want to have it comfortable. Ok, I have to stop my normal shower routine. But I would bet that it’s rather a good 5 minutes and without dawdling. The temperature on the thermostat of the mixing valve is 42°C. Whether that is really true I can’t say, and the rain shower is much colder than the hand shower. I think that’s due to the rain effect and actually the longer distance the water falls from up there onto me, but I wouldn’t have thought it was that extreme before. Does anyone else know this effect? So same fixture, once fixed showerhead once hand shower and despite thermostat valve different temperatures?

We also have both on the fixture, set to 38 degrees. It feels the same.

OK, may I still ask how tall you are and at what height the rain shower head is, or rather the distance from yours to the rain head?