How much additional cost according to the structural engineer's calculation?

Why can't I add clay to the basement wall anymore once the basement is standing? Whether contaminated soil can be used on the property is apparently also a question of the region. In my case, no one took soil samples before I had the pile spread in my garden. Nobody cared a single bit.

Because waterlogging that cannot drain away is bad even with great sealing. OK, one might think that the clay soil also repels moisture, but it is not that impermeable. And then frost shattering and underwashing right at the house wall are also bad.

Why can’t I add clay to the basement wall once the basement is built?

Because then there will be settlements around the house for years. Usually, this is the area where paths etc. are laid.

In my case, a foundation base for a lean-to roof was installed in an area where clay had been backfilled underneath. Overall, the foundation tilted crookedly five times due to underground settlements and had to be repaired.

I'm always surprised here. A foundation is never actually made on the ground you find, right? A certain depth is always dug out, gravel or sand is poured in, and then compacted. What sense would it make to dump the excavated soil back into the construction pit?

If you dig a 3m deep hole, you have to slope the sides. At least, if you're not my general contractor, who "sloped the cistern vertically." But that's another matter when people are working inside. And whoever builds formwork for the floor slab and erects basement walls also needs to be able to access it from the outside. With a one-meter working space, a 10x10m area becomes 12x12m, or about 44% more excavation than the footprint calculation suggests. Plus the slope.
Once the basement is standing, you refill the outside again. But due to compaction and infiltration, only rarely with the original excavated soil.

By the way, sometimes you can be cheaper off. Around here, large trucks often drive around asking if someone still needs this or that pile of soil. They apparently load it up and sell it privately for cheap... bypassing landfills, etc.

You have the wrong scale there. A 10x10m basement with 1m working space becomes 12x12m, which at 3m depth is about 450 cubic meters. For the slope, you quickly add another 100-150 cubic meters. Natural soil weighs about 1.7 tons per cubic meter, so we're talking about 30-40 trips with a large semi-trailer tipper. From fill soil that the gravel pit sells for €2 per ton after having accepted it at a high cost. The business model might work with topsoil, but not with clay. Not to mention that you can also find excavated soil directly from private individuals in classifieds.