Well - Technology, Systems and Costs

Yesterday I found out that we need a rainwater infiltration system. This raises the question for me whether we might as well install a cistern underground to have a small water reservoir there. This covers the hot summer days and the rest comes from the tap.

This would definitely be an option if you are required to build an infiltration system.
You have already found the current thread on this topic.
You should clarify / check whether the rainwater must be completely infiltrated, or if you can possibly discharge an overflow from the infiltration system/cistern into the sewage system.

from the other thread:

Even if you always plan with a buffer, it is money that ends up missing somewhere in the end

Well – normally something like this is in the development plan. Since this is often provided before purchasing the property (you could have inquired, if applicable), you could have informed yourself and planned it into the budget. (Smart-ass mode off)

From my point of view, this would have settled the issue with the well anyway.

Infiltration and cistern (=retention) are to be seen as independent of each other, at least initially. Maybe when installing the infiltration, if it is to be done underground, e.g. as a soakaway, smaller synergies can be gained when setting the cistern. But I really don't believe in that yet. see below.

That means the well belongs in the same category as cistern or domestic waterworks: either it is there anyway or prepared for other reasons, otherwise not financially worthwhile. Water is just too cheap.

In response to my inquiry about the costs associated with using a pump, I received the following answer from the region today (to me, this initially sounds very good and cheaper than an external water meter):

"...according to § 46 of the Water Resources Act (WHG) and § 86 of the Lower Saxony Water Act (NWG), the extraction of groundwater for garden irrigation in small quantities is permitted without a license. Small quantity here means the extraction of up to 10 m³ per day. Therefore, no fees are incurred...."

What do you think about this?

Sounds good so far, since you will NEVER extract 10 m³ per day (we use about that much water per month).
The cost block for well construction and electricity for the pump remains unaffected by this.
What remains questionable is: Would you possibly have to prove the amount extracted? I can't really imagine that for a private household, where apparently less than 10 m³/day is extracted.

As already said, a pump, cistern, etc. only make sense if you can do the work yourself cheaply or if everything is already available anyway. Rather, it is always the idea of a higher ongoing additional cost that deters people from pumping tap water into the garden. A 5sqm plastic basin is dug into the garden for 1500€ material cost + labor costs (if directly integrated into a larger project like house drainage, etc.) + garden pump + pipes, only to empty the 5sqm in summer and then have to switch to tap water anyway because it hasn't rained in the meantime (this often happens in summer). Even if it really works well and you can always take water from the basin, you will hardly save more than 5-10sqm per month (you have to consider that it has to have rained for the 5sqm to be refilled – consequently less watering effort). Over 4 months, that adds up to about 40sqm saved per year. 1sqm of fresh water costs 1€ (and about 3€ disposal). So, that's 40€ saved per year. With the 3000€ acquisition cost such a 5sqm unit costs including pump, etc., you can extract water directly from the tap for 75 years. Other advantages of fresh water: no pump blockages, no pump maintenance (possibly costs), drinking water quality from the faucet (you can take a sip or fill a paddling pool without problems), etc. Consequently: plan a meter for the outdoor water connection to save wastewater charges. That then costs 40€ more per year in running costs, but you can save several thousand.