Let’s attack this from another direction.
The figure that O’Neill used in that NASA report that I cited above was that each person requires 157.1 square metres of deck for lifetime residence in a civilian habitat with recycling and agriculture. (SP 428, p.35). That’s 6,365 people per square kilometre, a shade fewer than Copenhagen or San Francisco, 30% the density of Paris. If the Old Capitol had more than 267 square kilometres of liveable space it would not yet be overcrowded. If the SHQ habitats had less than 51 square kilometres of liveable space they would already be over-occupied.
Suppose that the Old Capitol was built for a nice round 1,000,000 people, so that it is clearly insufficient for the 1.7 million current population of the New Capitol. The designers would have aimed for a deck area of 157 square kilometres. Supposing that the deck is as long as its circumference that suggests a cylinder 12.5 kilometres long (excluding the end-caps) and 4 km in diameter. Suppose further that the designers specified 10.0 m/s² pseudogravity, 100 kPa of breathing mixture at 29 g/mol, and ambient temperature of 290 K, with 10 tonnes per square metre for radiation shielding, armour, buildings, and landscaping and a safety factor of two on the strength of the structural hull.
That structure could be built of high-tensile steel, and if built of high strength aluminium alloy it could have a hull only 2.78 metres thick massing only 1.6 billion tonnes. Looking at “futuristic” materials, graphite-fibre-reinforced epoxide resin could do it 1.03 metres thick and 280 million tonnes. Diamond and pure oriented buckytubes are GURPS TL11 materials, and even buckytube-reinforced polymer sounds a bit speccy. Let’s suppose that a GURPS TL10 structural material could be five times the tensile strength of high-tensile steel (“nanocomposite” armour is five times as effective as steel) and about 1400 kg/m³. I calculate that that would suffice to build the habitat specified with a structural hull 0.48 metres thick and massing 140 million tonnes. “Nanocomposite” armour in GURS Spaceships is G$33,333 per tonne, so the structural hull of the Old Capitol might have cost something like G$4.67 trillion. That’s about ₢1.6 trillion, which is surprising affordable out of Imperial revenues, which even back then might have been in the region of ten times that, per year.
Then make the SHQ habitats 10 km long (plus end-caps) and 3.18 km in diameter for a nice round 100 km²: they’ll fit 637,000 people, which is okay for the 322,000 that the average SHQ calls for. Structural hulls 0.38m thick, 71 million tonnes of structure supporting up to a billion tonnes of fit-out and 100 million tonnes of breathing mixture. Cost about ₢789 billion each, or ₢16 trillion the set.
The when it comes time for the New Capitol, lash out on 1,000 square kilometres, enough for 6.37 million people at space-habitat densities, but cut the design load to 5 tonnes per square metre. Make the habitat 31.6 km long and 10.1 km across. That calls for a 1.8-billion-tonne structural hull consisting of 0.97 metres of nanocomposite and costing about twenty trillion crowns. Plus which five billion tonnes of fit-out and 3 billion tonnes of air.
(A 4,000-km² structure would cost about ₢178 trillion, and might be considered an extravagance.)