Photovoltaic system: How many kWp are enough for a house?

Sun + not too warm is just perfect. In midsummer at 35 degrees, the efficiency drops because the temperature can no longer be dissipated as well (this is often compensated by more hours of sunshine), but a consistently sunny April is of course the best! It has also been the best month for me in a long time, better than all other months last year, and last year was already extremely good overall.

By the way, the dryer consumes 6 kWh

That is extremely much, if that's correct. Modern heat pump dryers use about 1-1.5 kWh per drying cycle.
That means saving 5 kWh per cycle at 27 cents per kWh = €1.35 savings potential per drying cycle.
A new purchase pays for itself very quickly.

We had by far the best month since 2017 here (steep south-facing system) in April. For you, with the east/west system, it could get a bit better in the summer, but the sunny, cool days of the last few weeks were really great in terms of generation.

Yes, I am aware of that. But honestly, with my large system, that’s not so relevant. It still produces between 2 and 4 kW even when it’s heavily cloudy, and with my own consumption, I rarely go above that.

I can already take that idea away from you. You just have to consider that from the time change on, after 5 pm nothing comes down anymore and all the household action only begins then, not counting the heat pump yet (at least for us, or do you have gas heating?). You can only mitigate this by putting the dryer, washing machine, cooking, and baking in the midday hours. And even then, without storage, I don’t assume 40% self-sufficiency on average over the year.

Well, in the old house we have (unfortunately) a gas heating system. So no heat pump. With a heat pump, of course, things would look completely different, no question! But even then, I could cover a lot of my own electricity needs with the system if I only ran it during the day.
Cooking doesn’t happen in winter for us because we have a wood stove. So in the dark months, maybe every two weeks the electric stove is used; otherwise, everything is done with wood. The dryer basically never runs for us since the little one is out of diapers. And we can very well time the washing machine/dishwasher.

Well, in July something will be changed here again. Since the whole house will no longer be occupied by family and we will rent out an apartment, the photovoltaic system will only be connected to our apartment. And from then on, I can observe a whole year and will be wiser a year later about how much we really manage. I believe it will come out to around 60%, but that’s just a guess from someone who only recently got a system. And I know the estimate is very optimistic, but I know

Here are the promised values from yesterday, the first day. Until sunset, we had 65% self-sufficiency. Then showers were taken and hot water was prepared (air-to-water heat pump). Heating has not been integrated yet (SmartGrid). Otherwise, no hot water preparation would have taken place.