After my first thoughts and research on YT, I quickly came across the site of the European Commission and PVGIS. With this tool you can simulate your theoretical yield.

I would like to present my results here:

  1. Performance of grid-connected PV
    Simulation outputs
    Slope angle: 65 °
    Azimuth angle: -50 °
    Yearly PV energy production: 721.24 kWh
    Yearly in-plane irradiation: 1076.2 kWh/m²
    Year-to-year variability: 44.92 kWh
    Changes in output due to:
    Angle of incidence: -3.11 %
    Spectral effects: 1.89 %
    Temperature and low irradiance: -5.71 %
    Total loss: -16.23 %
    The basic settings I have assumed are:

        Installed 820 Wp
        System loss of 10%

    The simulation results in a potential energy amount of 721 kWh per year. Which, at an electricity price of
    0.33 €/kWh, this corresponds to a saving of 237.93 €. If I now assume a self-consumption of 90%, it is still €214.

    Monthly energy output from fix-angle PV system.

    Here you can see that even in good months, an average of 3 kWh per day is not achieved. For example, in July with 87.3 kWh/month and 31 days, the result is only 2.8 kWh per day. Since these are average values, it can of course still come to more than 3 kWh/day on some days in summer and less on others (rainy days).

  2. Power production estimate for off-grid PV
    The simulation of the off-grid PV system is actually not correct for my case but if I only want to see the approximate expected amount of energy per day, then this can be created as follows.

    I enter 820W as the PV power and then add 1 Wh of daily consumption and 1 Wh of battery capacity.

    What I can expect is a list of the energy not needed per day. That is, what I can generate on average on one day of the respective month.
  3. Summary
    As you can see, after the first observation, the yield is significantly less than assumed with 4 kWh per day. Of course, this was only a mind game and the simulation should be much more reliable. So with my design of the system with 820Wp panels (2 x 410 Watt) and a VDE-compliant inverter with 600W, I get a yield of approx. 2500 W/day in the summer months. Which, however, will drop to 570 W/day in the winter months.
    As a consolation, I can assume a fairly high self-consumption rate, so that, as shown in point 1, I can expect a revenue of about €214 per year.