What should be considered, or on which points do we or the construction companies need to coordinate?
There is the famous Goalkeeper thread about the adventure with a worst-case end-terrace house (which is basically what semi-detached houses are, too). Otherwise, I have already summarized all the essentials in all of my posts in semi-detached house threads, see as well as and
Technically, a profile match at the "joint" is already sufficient to ensure the best possible fit.
Of decisive importance is the coordination regarding the basement issue, namely that in "crooked" semi-detached houses the party who builds the shared basement builds BEFORE the one without a basement. Profile congruence (i.e., having the same roofline over as long a distance as possible) is the second "most important" point. Ideally, as already said, you choose the same shell construction contractor. In your case, that would mean also building with Schwabenhaus, at least as a "shell house" (if you are bold enough to want to seek your salvation in self-managing the finishing trades).
In the posts listed above, there are also references to external posts by me on the subject; when googling, baulotse-hoffmann should now be replaced by bauen-jetzt. There you will also find "The Stone Mantra of 11ant" regarding your original question. I myself have lived for ages and through several properties predominantly in pumice in my area; the difference to lightweight expanded clay aggregate is ultimately somewhere behind the decimal point despite the different origins, the building materials are at least cousins.
Construction contractors usually have one and a half preferred wall building materials: with one they have the most experience, and they use the other in special cases or when their preferred material temporarily has a less attractive purchase price that would spoil their calculations accordingly. And some of them disparage with scare stories whatever is too expensive for them to buy or whatever they have too little experience with. There is no philosopher's stone or Columbus's egg, but neither is there a devil. Likewise, I have no concerns about a timber frame panel builder like Schwabenhaus. So feel free to examine, with an open mind, whether that might also be something for you. I am happy to personally accompany the project as well.