How large does the photovoltaic system need to be?

The question is what sufficient means. Your main yield is in summer, electricity is mainly needed in winter.

Briefly the material prices for the solar installer:

Photovoltaic modules from 400€/kWp
Mounting ~120€/kWp
Hybrid inverter ~2k€
5kW storage 4k€, 10kW 6k€
plus cables, small items flat rate 1k€

Then there are scaffolding and personnel costs...

If you can build large and compare a few offers, the feed-in tariff still pays off the system 100% in 2022. Self-consumption additionally increases profitability enormously. With which other part of your house did you have such high subsidies?

That means completely independent of consumption, you should always cover all available roof areas (including north, 25°, and flatter) as well as garages and carports.

Small chain of thought impulse:
The system lasts at least 30 years.
In 10 years no one will voluntarily drive combustion engines anymore.
Photovoltaics deliver about 5-10% of the installed capacity in bad weather.
Electric cars only start charging at 1.6 kW.
If you also want to drive cheaply in bad weather, then calculate now.

The question is what sufficient means. Your main yield is in summer, electricity is mainly needed in winter.

Briefly the material prices for the solar installer:

Photovoltaic modules from €400/kWp
Mounting ~€120/kWp
Hybrid inverter ~€2k
5kW battery €4k, 10kW €6k
plus cables, small parts flat rate €1k

Then scaffolding and personnel costs...

Are the prices with or without VAT?

Even if the offer price of 25,000€ incl. installation and VAT is, there would still be 5,000€ too much.

Gross prices in this case

the <7Cent production costs (feed-in tariff) including installation and ongoing costs is probably only possible with self-installation.

So I am seeing this correctly? 10kwp with 6kwp storage including installation should be achievable for a maximum of €20,000 gross?