Infiltration of rainwater, which method?

depends on the size. Although in this case, of course, you would use the most permeable soil possible. But the contractor also wants to make a profit somewhere.

For comparison Rigole/Iglu: Was everything considered for the Iglu or only the prices for the Iglu taken?

Only the price for the igloo was taken.

The item with the pipe also refers to the [Rigole].

There is probably more at the infiltration trench that you probably haven’t considered yet for the [Iglus]. You also need maintenance access, ventilation, and fleece for the [Iglus] so that they don’t clog up. That way the prices become relatively similar quite quickly. An advantage of the soakaway boxes is also that they can be built "deep down," while [Iglus] can only be installed horizontally.

So I quickly searched now, it's not that expensive. And it seems to be complete.

Then please try to get a calculation according to AW 138 for that.
And honestly, there should be a difference between OBI goods and something from Graf, Intewa or similar.

Yes, that's probably true, but "no name" products don't always have to be bad.

For the skip, a volume of 3.3m³ was calculated.