When you think about how advanced Federation technology really is... the Yorktown starbase is really not a big deal to design and construct (in a short span of time). They could have easily made just 1/8th of the station and then reproduced it in a spherical fashion with automation doing everything (which could have taken days or weeks - given how automation is hundreds of thousands of times faster and better than people in reality, and Trek would be progressing faster than exponential by the 23rd century giving them far superior capabilities).
Any advanced space culture would have to rely on automation for construction in space (considering its very dangerous and manual labor in contrast is too slow and inefficient).
The Federation in the 24th century (prime timeline) might have had the Yorktown station as well for all we know. There's no reason to think that the station wasn't already in existence before the events of 2009 Trek movie.
As for it looking a lot more advanced than DS9... well, DS9 is Cardassian in origin, and a mining station to boot.
Starfleet did have the mushroom type starbase orbiting Earth in the 23rd century (and that was pretty big too)... and for all we know, it could still exist in the new timeline (seeing how Earth's orbit is really, REALLY huge and you could easily place thousands of ships in orbit without seeing them from a distance).
Though, it could also be that due to events of temporal cold war during Star Trek Enterprise, certain changes in Starfleet designs could have ensued (the destruction of the Kelvin could have affected a pre-existing superstructure in orbit of Earth - unless it didn't and Starfleet merely chose to make a newer starbase design that would co-exist with the mushroom one and the mushroom design might have been phased out eventually).
The Yorktown does make a good sense as a staging area as well as a diplomatic hub for introduction to the Federation way of life (plus it probably has decently sized and dedicated construction facilities for creation of ships and fleet deployments - so I doubt its only purpose is for diplomacy [although it is more than likely its primary function given how the Federation works) - like every other piece of SF technology/hardware/ship, it seems multi-factorial in purpose - and that's good).
But we also have to keep in mind that the Federation is likely more than capable of making mega-structures... its just that they likely have little need for such things given they usually do more with less (technical efficiency) without thinking about 'money' - its more to do with doing things in abundance sustainably with little to no damage to the environment while using state of the art science and technology - something that Capitalism doesn't/can't do at all since in Capitalism, focus is on 'cost efficiency' and SF technology reflects technical efficiency instead).
At any rate, the design of the station (aesthetics) could partly be there for the purpose of impressing potential alien races that might consider joining the Federation, even though it may not look too 'logical' - and to the Federation it may not matter as they could have reinforced it really well either way.
Maintaining artificial gravity, as well as atmosphere could be contained to the stations 'arms' and not throughout the empty sections of the structure (after all, you would want to do things efficiently, so there would be no point in filling the entire spherical area with air), while the blue haze could be a physical transparent structure (possibly made of incredibly tough material for additional protection that was lined with tough shielding) for generating daylight and giving an illusion as if you're on an planet.
And it is possible that the stations arms also produce an atmospheric effect of their own to hide the outer space even more.