I also have issues with use. What is the point of rings arranged like that? They can't rotate around each other, unless you set it up more like a multi-axis trainer where each ring is smaller than the next, and can rotate within them. But that seems a bit derivative to me, and wouldn't provide the direction of rotation needed to induce gravity or something.
Instead of rotating sideways like a gyroscope, why not have them as free-floating rings that are spun like wheels around the central sphere? They could be held in place with minor corrections by tractor beams, and spun by using oscillating repulsor beams generated by the central sphere. The sphere would house a massive engineering section containing the warp core and all the power and weapons systems of the station, and also immense transporter facilities. The rings wouldn't be physically connected to the sphere, but would receive power and people could transport back and forth.
The idea is that the rings would have massive tracks of cheap housing and cargo storage by saving on energy costs from not having to generate artificial gravity (gravity would be simulated by spinning of the rings). This type of design would maximize space while using the minimum amount of materials. Spheres by nature contain the greatest volume within the smallest physical space than any other 3D object. The rings would be modular extensions of the sphere, and since there is no need to build pylons to connect them to each other, new rings could be added as necessary, each built to maximize space and energy efficiency.
While the tractor and repulsor beams might use more energy when constantly running than artificial gravity generators, once the rings get spun up to speed, the beams would only have to run intermittently for distance and speed corrections. This would leave more energy available to run shield generators and weapons systems, making this more of a dedicated Battle Station, rather than a starship drydock like Utopia Planitia or a refinery/cargo dock like Deep Space Nine.
The rings might also have extensive shuttle bays, as in the event of a power core failure, the inhabitants would need to evacuate the rings.