Payment plan is somewhat okay or clearly optimizable

I wouldn't say that so categorically. Some GCs are quite open to adjustments, while for others it is "set in stone." Therefore, the only thing that helps is to coordinate with the GC and present your arguments. The contract most likely won't be signed at the notary anyway, so it is sufficient if the GC accepts the changes.

Either way, I would mentally plan for the real estate transfer tax for both the property and the house under the described circumstances.

The property is registered under someone completely different. I even became aware of the property owner before the house provider.

Believe it or not: The tax office does not care whether the same person/company sells the property as the one who also builds. As long as there is a compulsive connection between the purchase and the choice of the builder, they will come looking for their share. There is also quite a bit about this in the forum, and contrary to popular belief, the tax office is not stupid.

Can you link me the thread?

The search here in the forum with the terms "Grundsteuer" "Bauträger" helps.
Search:

A special post from the results:
https://www.hausbau-forum.de/threads/erst-Grundstück-oder-bv.13994/#post-108356

I could get endlessly upset again about why it actually makes a tax difference whether I have the house built by another company or by the one that sells me the land. But unfortunately, getting upset doesn’t help...