Offer for photovoltaic system including storage - Storage yes/no?

You should definitely get somewhat familiar with the future policies regarding photovoltaics. Starting in 2025, there will no longer be a fixed feed-in tariff; instead, the stock market prices will be used. In other words, in the morning/at noon, when the sun is blazing, you won’t get anything for your electricity anymore. In the evening, you use it yourself, when you would get a lot for it. This will happen in stages starting in 2025. No one knows exactly yet up to which photovoltaic size the fuss will be scaled down (my latest info).
So, take a look at your consumers. Heat pump? Is there an electric car present or planned? If yes, is it usually charged at home around noon?
If you don’t have enough consumers, I would get a small storage system. They are currently quite affordable.
That way, you don’t have to give away the electricity at noon.
A modern house usually has a standby power consumption of around 300 watts. As soon as cooking or washing is happening, it quickly rises to 5000 watts. An electric car gladly pulls 11,000 watts (11 kW).
Given the planned policy, I would recommend filling the roof only with caution. Depending on the number of consumers. Otherwise, you have a full system and give away the electricity around noon. But some people are so unselfish and like to do that gladly.

Fill the roof completely. You can also simply retrofit the storage. If I had space (where it doesn't bother me visually), I would immediately install another 50kwp or so.

If I had space (where it doesn't bother me visually) I would immediately add another 50 kWp or so.

If, if, bicycle chain.

You first have to get the 50 kWp approved by the grid operator. Nowadays that's not so easy anymore. Unfortunately, the power grids in Germany are dilapidated.

And if you want to retrofit, you start all over again. Data cables, smart meter, remodel the meter cabinet, install storage, and also a new inverter. A full roof simply doesn't make sense.

It only really pays off with large systems and direct marketing.

Woulda, coulda, bike chain.

You first have to get the 50 kWp approved by the grid operator. Today that's not so easy anymore. Unfortunately, the power grids in Germany are dilapidated.

And if you want to retrofit, you start all over again. Data cables, smart meters, renovating the meter cabinet, installing storage and also a new inverter. Fully covering the roof just doesn't make sense.

That only really pays off for large systems with direct marketing..

Yes and no. Fully covering the roof can make sense if there are consumers in the household. In winter, you're happy about every watt. Of course, you can forget about charging the car with it. In summer, you then enjoy the charged eCar. But as I said, it highly depends on your own profile. Can the car regularly charge around midday? Do you have a heat pump? What does the garden (pool pump, garden pump, pond pump, ...) demand in terms of continuous power? Do you work from home? Do you also cook more often around midday? Do you have programmable washing machines and dryers and are you willing to use this function?
When we talk about "fully covering the roof," we usually mean systems of around 10-18 kWp. Those are still neat things. Most people only get beyond 20 kWp by including garages and sheds. Beyond that are the few who really have large houses with free roofs.

The old lady who does laundry once a week and whose biggest consumer is the stove/oven, of course, doesn't need a fully covered roof. A balcony power plant is probably enough for her.

I am somehow facing the same decision regarding the retrofitting of a photovoltaic system. I am also faced with the choice of a system with storage or a system without storage, or, for simplicity's sake, just a balcony power plant on the garage.

If you read various photovoltaic forums, the heavy contributors all swear by fully covering the roof and absolutely no "pointless" storage. If I calculate my "potential" system without storage, the electricity generation costs me about 7 cents over 20 years (without financing costs). This is just barely covered by the feed-in tariff and therefore only brings benefits through self-consumption. If financing costs are then factored in, every generated kWh that is not self-used initially becomes a loss. Therefore, I am not sure if this "forum opinion" still firmly holds from times with higher feed-in tariffs. In addition, this calculation is, of course, only based on current prices. If a price increase (which, in my view, will come in any amount) is factored in, the scale clearly tips, compared to with/without storage, towards higher self-consumption, and this can only be realized with storage.

Current situation with me: My heat pump is unfortunately not controllable. Currently, there is a hybrid vehicle and a purely combustion engine vehicle. However, the electricity demand will probably increase over the next 20 years due to electric cars.

I must admit that (even though I work with numbers daily) I cannot sort out all the many variables (share of self-consumption/level of future demand/price increase/lifespan of storage and others) and I find it very hard to make a decision because depending on which variable I adjust, completely different results come out. Then I think again we simply make a balcony power plant on the garage and thus reduce the base demand, and that’s that. This definitely pays off within a very short time. And then the "green" conscience comes back....

Not yet considered in the consideration is price-based charging of the storage/car in combination with variable electricity tariffs.

If I calculate my "potential" system without storage, the electricity generation costs me about 7 cents over 20 years (without financing costs). This is just about covered by the feed-in tariff, and therefore only brings benefits through self-consumption.

Then just calculate with 20-25% self-consumption. What do you get then?

And about the storage:
Just calculate 4,000 charge cycles in 20 years (that is 2,000 kWh per annum or 40,000 kWh over 20 years for a 10 kWh storage).
Saved electricity costs at the current 25 cent electricity price = €10,000
Lost feed-in tariff at 8 cents = €3,200
Profit = €6,800 (without price increases)
Can you buy and finance the storage at this price over 20 years? Will it fail once in 20 years? Can you achieve 40-45% self-consumption then (especially in winter you hardly get the storage fully charged, and in summer not fully empty) or do you cannibalize the self-consumption that you have without the storage? Storage losses / efficiency are also not yet calculated.
Or calculate the other way round. If the 10 kWh storage costs €10,000, the stored and reused electricity costs you an amount of X cents ==> with my example with 4,000 charge cycles, that is 25 cents per kWh (!!!). You can also calculate with more cycles, but then with about 5% losses in charging/discharging.
But in the end, it almost always turns out that the prices currently asked by dealers for storage make the use uneconomical. If you can somehow get it cheaply yourself and/or have someone who installs it under the table, the situation can change.