Construction report single-family house 1200 €/m²

Where did you find that Bims is supposed to have 52dB? I just googled it and only found one report saying that the sound insulation of Bims is supposed to be poor....

I found that at Bisotherm and KLB, or am I interpreting that incorrectly?

Bims is that lightweight stuff that floats on water. Without googling, I absolutely can't imagine that they have the same DB values. Since sand-lime brick easily has 10 times the density and mass, more mass means more sound insulation.

I also believe that sand-lime brick provides significantly better sound insulation than pumice. If we build, we will only use sand-lime brick for the masonry.

or am I interpreting that wrong?

This is not pumice. The specified stone has a bulk density class of 2.0.
Commercially available pumice building materials range from 0.5 to a maximum of 0.8.
In your stone, pumice may be present as an aggregate. However, most of it is likely (lightweight) concrete.

Yes, from that point of view I would definitely change your "Bims" wall inside again .... we can clearly hear the children through 17.5 cm bricks, so I would also only recommend KS.