Is a new construction possible with our cost estimates?

We also have no land costs, as the family wants to enlarge their plot and will then gift us half of it.

turnkey developer.

then it is not a developer! Please remember for legal questions and rules: a developer sells a house with land and is the builder himself, a general contractor builds your house on your land.

In the case of a gift, it goes to you, and - I am less familiar with this - not to your husband. He will then not own a house, because a house belongs to whoever owns the land. Not automatically to the one who signs and pays the financing.
If necessary, this issue should be discussed again with you and a notary.

The base house costs approx. €212,000

Are €1900 / sqm very unrealistic for "almost" just the pure construction of the house?

Yes, that is a catalog and advertising price, a so-called bait offer. You indirectly say it yourself with the “base house.”
Who is the construction company? Town & Country? Do you already have the building service specification?

The earthworks include 30 cm excavation and 30 cm backfill with gravel and compaction.

That means you have to bear at least the 50 cm up to the frost-free zone yourselves. Also the removal and disposal, which will be necessary.

The driveway is about 3.70 m wide at the narrowest point (entrance area) and gets wider afterwards and is still paved.

You have to expect that the utility company will have to dig up the paving along the length for the connections?

That overlapped

So far, we are interested in Team Massivhaus from northern Germany.

Team Massiv has the reputation that they now offer a fixed price. Later, when construction takes place, certain things will no longer be included and must be re-specified at a higher price. This can be read in many construction blogs.
Otherwise solid and neutral construction. Rather inexpensive materials. I would calculate a decent buffer. €50,000?! For brickwork, a significant additional payment may be due.

That overlapped.

Team Massiv has the reputation that they now do a fixed price. Later, when building, this and that are no longer supposed to be included and it has to be newly priced at a higher cost. You can read about this in many building blogs.
Otherwise solid and neutral construction. Rather inexpensive materials. I would calculate a decent buffer. €50,000?! For clinker bricks, a good additional payment might already be pending.

Thank you very much for the advice regarding the construction diaries.
Is there a general contractor in the northern area that one can often rely on?

And also regarding the removal of the paving stones, I still have to consider this and had not thought about it.

Is there a general contractor in the northern area whom one can often rely on?

Which northern area are you from?

In the case of a gift, it goes to you, and - I am less familiar with this - not to your husband.

Just for your information: gifts to in-laws are also exempt from real estate transfer tax. Whether the parents want that is another question. Personally, I think it’s a bad idea if both take on the financing or repayment, but only one is the owner. What you can do in such cases are retransfer reservations or clauses in the gift contract (to be able to simply kick out the son-in-law in case of divorce or similar). Not that you necessarily need something like that, but it’s good to know that such options exist.

From which northern area do you come?

We will be building in central Schleswig-Holstein.