The living space is approximately 8 m² smaller in the application drawings compared to the draft (GU).

That’s exactly what it’s about. Were these sketches created specifically for YOU, or are they sample sketches that are generally used when deciding on the type of house / floor plan? In connection with the clause you quoted from the contract "taking precedence over drawings," this is exactly the decisive factor in whether you can derive a claim or not.

It is certainly not my intention to judge you in any way. You won’t find a single word where I do that – verifiable.
Under no circumstances do I want to encourage you to recklessly run into a wall out of anger and disappointment. I would find that unfair. Some things are easy to write when you do not bear any risk yourself. But the situation between you and your building partner is tense in such a way that the solution can decide whether you get through the construction well and satisfied or not.

If it is clear that the colorful drawings you refer to were created individually for you and thus were an essential part of the consultation, you have a chance to achieve something or to withdraw from the contract. If you don’t know that, you can find out. If these images were not created specifically for you, communication may have gone wrong, but a dispute about it would do more harm than good. This difference is subtle but important.

That’s how it looks. The question is therefore whether consent for the change of the living area was required concerning the “colorful drawings.” This determines whether there is an actual "reduction of the living area" or whether the comparison between the living area on the colorful drawings and the contractual drawing is even relevant.

And to @11ant yes, he was in the construction industry but not really successful. So ignore what he says.

No, the plans are the basis of the contract. The contradictions of the masses only make it worse for the contractor, not for the consumer.

And seriously, these are not additional costs for the contractor.
8sqm more base plate - 500
8sqm more screed - 200
Heating - he won't lay a single loop more because every room is a few cm wider.
Parquet: you can offer to take it over.