I don't know how the tunnel is dedicated.
OSM does not indicate any road number for the tunnel route. I guess that H13 and H14 should be routed through the tunnel but is H4 routed through the eastern branch (makes sense since it's the shortest route) or through the tunnel (as indicated on wikipedia) and via the western branch?
I only read that the E54 should be routed through the tunnel. That makes pretty much sense and it's the only change I make now. Rest is waiting for more info.