Scaling "Stroke" Effect "Brush Size" while scaling composition?
Easy fix, you see the small sun icon on the imported comp layer? Disable that, that basically means that the comp should act like the layers within it should act like they are in the parent comp. It negates the transformation your are applying to it and the effect will just keep its pixel value its supposed to have, you are not "blowing it up" like you would expect.
If you disable it the imported comp will act like a rendered video.

If you have huge pixelation going on just go to full resolution in the preview and it will be fine, though the layer will not act like a vector, you will have a rasterized image so keep in mind to have a big enough resolution if you want to scale it up.
Better to have it bigger and scale it down than having not enough.