Is the solar system on the roof worthwhile?

If you install solar thermal completely by yourself including buffer storage and appropriately larger size, it can financially pay off quite quickly through the BAfA subsidy.
With external installation, only if you have a very high demand for hot water.
I'm too lazy to do the calculations for photovoltaics now. Anyone can do that themselves.

Regards, Joe

What does "worth it" mean to you? Compared to which other types of investments or which ROI?

At least an amortization of the costs over the lifetime. But it would probably make more sense to set 3-4% p.a. as a minimum.

Then just calculate costs divided by lifespan in years plus costs * 0.035 and see if that becomes your annual yield. The whole thing only becomes difficult if that is not the case and you have only calculated with the current electricity price and made no estimate for the future...

Many people make the result look better with photovoltaics by assuming too high a self-consumption. That is perhaps also the factor that is the most difficult to estimate. I would say for myself that photovoltaics is worthwhile if it pays off after 15 years WITHOUT consideration of self-consumption.

It cannot be answered generally without knowing the entire system. With photovoltaics, a lot depends on self-consumption, as already wrote (but it also works without). It fits well with heat pumps or households with other large electricity consumers. With solar thermal for domestic hot water, you are well off if there is a lot of bathing, whirlpool or pool heating involved. The hot water is stored in fairly large buffer tanks, which make sense with gas/pellet heating systems, less so with heat pumps. Solar thermal for heating support is, in my perception, always viewed very critically, because solar thermal delivers a lot in summer but no one turns on the heating, and the opposite is true in winter. It seems like a dumb system (also quite high investment due to the size of the collectors).

If I may interject here. Also keep in mind that with a photovoltaic system where the electricity is fed into the general grid, income from commercial operations is generated, which requires a tax return (if you haven’t filed one yet, this might be relevant). Photovoltaics are more effective at utilizing the generated electricity. The depreciation period, if I remember correctly, is 20 years, for solar systems it is 10 years.