Construction costs are currently skyrocketing

Again: A cistern is something diametrically different from a soakaway and neither can replace the other – that’s exactly why they are combined: the cistern can ONLY store (and that with a hard limit) and cannot infiltrate anything, and the soakaway cannot store anything and can ONLY infiltrate (and that unlimitedly as long as it is not sealed). You need a soakaway anyway, because no cistern in the world can last the year without an overflow. If I want, I can buffer or temporarily store the soakaway inflow with a cistern. Neither is in any way an alternative to the other. The only thing that is technically an alternative to each other is “infiltration” vs. “sewer discharge.” Since the latter is prohibited here, I have to build infiltration. If I want, I can combine that with a cistern.

1. As already with the topic of photovoltaics: There is life outside of Excel. It simply brings me joy to be able to water my garden with rainwater and not have to use drinking water for it – even though here in the district we absolutely have NO drinking water shortage and by saving drinking water I can at least save money but cannot change the drinking water shortage in Brandenburg. Different people, different goals, different solutions.
2. It matters enormously in the amortization calculation whether you look at retrofitting an existing building or new construction. If I retrofit a cistern in my existing house, I have double the costs as in my new build but only 1/3 of the yield because I can only channel a fraction of the roof area. And in new builds, I regularly see people who spend weeks selecting the best steam oven and the best extractor hood and invest huge amounts of money in it – but no time or money is left for infrastructure.
3. There are municipalities that subsidize everything that buffers temperatures/water/electricity significantly. A greened garage roof definitely brings me even less return than a cistern, nevertheless I will do it and the municipality contributes to it. My cistern financially pays off after 15-20 years – regarding joy of life, it has already paid off.

And: regarding pump, what kind of pump do you actually need to get something out of a 3500l cistern? We have no fancy stuff like automatic irrigation, just a sprinkler and garden hose. I was offered an Al-Ko Jet 800 within my acquaintances. 20 years old, but supposedly mainly stored... 50 EUR. Is it any good?

The pump looks more like a domestic waterworks system to me. As long as you only have a 1/2 inch hose attached, the performance is relatively irrelevant; they should all be strong enough.