I noticed through the inspirational pictures you posted that you like your house to be simple, minimal, and unique. You like to incorporate original pieces into your interior making it one of a kind.
In the furniture board, you can see the mix between gray, brown, and little touches of khaki that work amazingly with the oak flooring. These colors mixed together can turn your house into a warm and welcoming place.
For the kitchen, I kept everything in white so it can brighten the space with a subtle light gray ceramic/granite flooring.
I added extremely original pieces mostly through the lighting design of this house. I chose elegant light fixtures that match perfectly with the space and the materials used, making it beautiful and well studied.
I recommend you to keep the walls painted in white and adding color through the flooring and the furniture.
I also advise you to use copper accessories, and maybe adding some greenery like cactus plants, they are very trendy in modern spaces right now.
Finally, I stayed within the budget; the total sum of everything is about 7188.89€ which is less than one third of what you had in mind :)
Hoping my design is to your liking, I would like to thank you for trusting me with your project, I enjoyed working on it.