The problem is that according to Science™ (https://www.bbc.com/news/magazine-20578627) with a tower of 2.17miles you start to get materials failure on the bricks. You might be able to engineer around this, but I suspect that the minifig-scale deathstar would cause the bottom bricks to melt.
That's true if you build the station on the planet, but I think the station is designed to be constructed in orbit in the first place. Its self-gravity should be negligible. Problem solved!
If I do my math correctly, the mass of the structure should be dominated by the surface, if it is constructed mostly hollow. There will be plenty of room to add individual rooms to play with inside.
The mass of the LEGO would be on the order of 113 tons assuming you build the surface out of 8x16 base plates. This is comfortably within range of a single Starship payload. It is much tougher to say how long LEGO would take to manufacture them, but I think it is safe to say that they could spin up additional manufacturing capacity for such an important national project.
It should pay for itself - you'd have a very long line of LEGO nerds buying tickets to help assemble it.
