Sizing of the house connection for electricity (for photovoltaic, heat pump, and charging station)

Does your energy provider even approve a 22kW wallbox?
35² is more than enough for 63A, which is 43kW.

More than 63A is difficult anyway with many utilities; it is often not understood why an ordinary single-family house should be supplied with the power of an average 8-unit apartment building... and in the end, the cables under the sidewalk or the street also have to handle it, otherwise the NH fuse will blow and the entire street section will be dark...

And whether 4 or 5-core... it costs almost the same because 5x35 is much more common and sold in larger quantities.

By the way, a house connection is not designed for all devices to run at full power simultaneously, and they do not do that either...
A 90s cooktop briefly draws 11kW when all burners are set to 9. Once the water is boiling, the burner only heats intermittently, and everyone can ask themselves how often they run 3 cooking zones at 9. This also applies to the oven or the coffee machine. The maximum power is not drawn continuously over hours.
This also applies to the kettle, which only draws its 2 kW for a minute to heat the water.

Such an NH fuse also has an overload characteristic; it does not trip immediately at 63A, but only at 1.25 to 1.6 times the rated current over a period of up to one hour, and for the large ones with 630A it takes even several hours.

You can imagine it like a highway. It is designed for average traffic, not the peak at the start of the holidays.

And last but not least:
Current-carrying capacity of 35mm² with 3 loaded conductors in earth (installation type D) is 98A.

As written by MachsSelbst, this is a standard connection for a single-family house in your case, protected with 63 A. It is also completely sufficient for you. We also have 100A connections for a small additional cost (I think it was 200€). You can do it if the extra cost is low. I did it, but it was also for a two-family house. To be honest, the 63A connection would have been enough there as well...

100A no longer carries 5x35² as NYY-J buried in the ground, then 5x50 must be laid.

63A is more than enough, especially since the future will or must be that devices in households, neighbors, streets, even entire districts are networked together and intelligently controlled or coordinated.

With the attitude "I want to draw my 44kW at full capacity whenever it suits me and for as long as I want," an energy transition cannot succeed.

I didn't write anything about the cross-section either. I can do without a discussion about the energy transition.

We paid about €700 extra to the municipal utility for the power increase from 50 to 63A. Would I do it again? Absolutely not. As previous speakers have already said, 50A is sufficient for a single-family house even with an 11kW Wallbox + heat pump. A 22kW Wallbox would also still work as long as it's not the middle of winter and the heat pump + co. aren't running at full power simultaneously.

In addition, with a 50A meter fuse (instead of the standard 35A), wiring with 16mm2 is sometimes required in the switch cabinet. My electrician also charged me a little extra for that.