The cantilever staircase does not hold, the stair builder is not a staircase builder

On the second attempt, the craftsman removed the concrete anchors

Properly installed concrete anchors are no longer removed. That already seems to be cause No. 1.

Is the bracket a purchased part? They look more like backyard DIY to me. The systems I know consist of 2 fixed anchors on the wall side of the bracket, which are glued into the wall and then additionally secured with at least 2 expansion anchors.

How is the stepping sound of the stairs, does it bang hard against the concrete wall?

As my teacher always said so nicely: "Mighty is the locksmith's power when he works with the lever!" I think this fits quite well here too.

From my point of view, several points come together. As you already recognized, the construction in your example image is much better for the dowel. The disadvantage is that the step must be formed so that the plate is not visible afterwards. During the installation of the steel dowels, I suspect an installation error. With correctly installed dowels, there is usually no slip, but a cone breakout of the concrete. My suspicion is neglected hole cleaning. I once had a 2.5-day training at Würth on dowel technology. We set two identical anchors, but only cleaned one hole. The difference was striking. The correctly installed dowel had the load capacity according to the data sheet and a nice breakout cone. The other was simply pulled out of the hole, with not even half the load capacity. The drilling dust should be imagined like chip gravel. What I also don't like is the very close spacing of the dowels.

If you agree with the company on a rework, insist that someone from Hilti, Fischer, Würth, … be invited before installation to make a dowel proposal.

How is the stepping noise of the stairs, does it hit the concrete wall sharply and loudly?

There was no stepping noise visible on the Pinterest pictures.

Normally, the anchors are concreted in.

The man, or you as well, should at least have a plan for the project regarding the materials (anchors, screws, steps...) as well as the execution and structural conditions (wall condition, etc.). Additionally, various calculations, since he surely did not just buy anything randomly. Do you have these detailed information?

Normally, the anchors are cast in concrete.

Of course, this requires appropriate planning, carried out by experts and implemented by professionals at costs that still allow the involved parties to live.

None of this was incorporated into this project. Unfortunately, the result speaks for itself.
No reliable advice can be given for an alternative solution because it is unknown how the structural integrity of this concrete wall was designed and how the staircase will be further treated.

I would immediately advise the OP to seek support from legal counsel; anything else will only delay the matter.