Are price negotiations with the general contractor still possible?

Giving a crash course in successful negotiation in the forum is hardly possible. Of course, two parties can come closer in an offer negotiation. That is clearly more than just asking for a discount or demanding one. Since you are apparently not experienced, the recommendation from to get upgrades or addons is probably the most effective way for you to gain added value.
To explain: A discount is 100% a reduction of profit. An upgrade or addon has for the customer the sales value and for the provider the production cost. If the provider gives you an upgrade worth €1000, it does not reduce their profit by this amount, but only by their production costs. If you have dealt a bit with the subject, you can especially benefit from upgrades or addons, which usually bring a very high margin to the provider - these are particularly cheap for them to add, and you get good value in return. That creates a win-win.

Just a completely stupid question: but what do you recommend in this area? Do you have concrete examples of what one can in good conscience try to get "on top"?

Just a really stupid question: but what is recommended in that area?

It’s not a stupid question. And quite specifically, you have to look at each case individually. For most companies, the pricing policy is such that the base products have a fairly low margin. The margin usually increases with the premium claim. With these thoughts in mind, you can see whether to step up a class in burglar protection or in flooring (as long as the working approach doesn’t change, for example due to huge tile formats), or in the bathroom fittings, or add a few more sockets (each at or near the locations already planned), a nicer staircase – these are fairly simple considerations with a high probability of success. Of course, it only makes sense if the upgrade is also worth something to you personally. As soon as these upgrades bring additional complexity to the logistics (e.g., a change of manufacturer as part of the upgrade), they naturally become expensive for the builder, since processes are disrupted.