I can apply paint to a cube, but not to my complicated object, even though I defined the material and I linked the image texture to the principal in the shader. It seems I cannot select anything in the UV map, so that might be the problem. (apologies but for some reason I cannot comment on my own question...)
First, you only connected an "RGB Node" to the "Principled BSDF color slot. You can't paint on a "RGB Node". For that you need a texture which you seem to have created above, but not yet linked. Connect that lonely "Image Texture" Node above to the color slot, replacing the connection of the "RGB Node". In your lower uv view the texture seems to be already selected, since it only shows the start of the name, be sure to select the texture itself, as the image and save the image before you start painting. Then, once you assign the Image Texture to the color slot it should make your object change the color to the dark gray shown behind the uv unwrapped mesh. From there all should work then, happy painting. And Blender can handle more then that, the more the slower based on the machine, but it's not the reason why it's not working.