Since there was no explanation yet. Based on my experience, the portal sky texture only works when being on the border of a visleaf. Hence, the comment for the necessity of a visportal.
So in my earlier attempt I just put the texture on a random brush in the middle of the map, which was then transparent instead of the skybox texture.
However, creating a proper door out of a portal sky brush is still tricky, when it comes to immersion. Once the door/visportal is opened the portal sky texture looses it's effect and will turn transparent. Which means, it works but looks strange to the player. So there should be a way to blend from the portal sky texture to the new texture from what you see behind. Also it might be necessary to stack two doors behind each other, that will be opend together, Otherwise you would end up having a transparent door from the side of the portal texture (once it's opened).
Even though the wiki was just mentioned when it comes to objectives. Alternatively you can also listen to Sothas calm voice