I try to tile the texture, so that the texture has the same size, independant of the size of the object.
Currently if I scale up the object, the texture also scales up.
This is an issue in shaders. I assume you are using the default shader for your materials. The default shader will use the object’s local coordinates (based on the object’s UV map). You will want to create a similar shader that uses something called world-space texture mapping. Depending on whether you use URP/HDRP with shader graph or the builtin (legacy) renderer, the instructions for this will be quite different. If you do a web search for “world-space shader unity” you will find quite a few results, but without knowing what your project setup is, this question is hard to answer directly.