I know Maginaryworld being 5-D is pretty much already accepted but to run through my current thoughts.
I do believe Eggman constructed four-dimensional space in his tower. The argument is that Eggman only constructed a model of a tesseract (which can be done by normal 3-D humans), but an actual tesseract has properties such as folding in on itself ad infinitum and constantly reshaping. Not only is the tesseract tangible, as Sonic and co. physically landed on it, but the world the tesseract is part of is one that is explicitly described as warping spatial laws and the laws of physics to reshape and fold in on itself ad-infinitum. Combined with Eggman’s experience with viewing 4-D space or beings from his adventures to Maginaryworld and his encounters with Solaris, and that the maze could briefly trap Sonic, who already demonstrated 4-D capabilities in his weaker Generations state by recreating entire space time continuum with his speed, I believe he could recreate the effect of 4-D space on a smaller scale like he did here.
However, since he warped the laws of physics to create this space, Sonic’s universe should not be 5-D, as Eggman likely artificially added an extra dimension.
But since Eggman can add extra dimensionality with his tech, I think it’s fair to say that both the Phantom Ruby dimension (which is called super-dimensional), and the Eggmanland Eggman would have created in Rush (which he stated would transcend dimensions), do qualify as 5-D, via four spatial dimensions and a temporal axis, as well as infinite size.
Eggman also describes his Ruby dimensions as his “dreams”, and he expressed a “wish” to make his dimensional Eggmanland. Wishes and dreams both qualify as worlds that can be made tangible. Since Eggman made both his dimensions with items on par with the Chaos Emeralds (and the Otherworld Comedy was after Test Run in release order), and since Cyberspace was made with and is powered by the Emeralds, Cyberspace should be able to contain a dream of Eggman’s caliber, especially since Eggman himself was inside Cyberspace, and Cyberspace absorbs the memories/dreams of those who enter. And both Eggman’s Dream and Cyberspace would exist in Maginaryworld, hence 5-D MW as well.
In the event R > F transcendence is still on the table, the Nights would become 3-D (via infinite amount of 2-D space + time component). Sonic’s world would have an extra spatial dimension on top, making it 4-D, but there is also an extra time axis to be distributed. The reason being that the time axis for the Nights would count as an independent origin, as the world and all of its features are controlled by text written in the book, including its space and time. So it’s origin is the text in the book, not the overall origin of time.
Since Sonic’s world, Maginaryworld, and Cyberspace are all disconnected, the extra time axis could apply to Sonic’s world and its equivalents, which would make Sonic and Blaze’s worlds 5-D. Everything above that would get a possibly 6-D rating, including dream worlds, Rush Eggmanland/Phantom Ruby, and Cyberspace. Maginaryworld receives a definitive 6-D rating, as due to its status as the largest temporal Entity in the verse, the time axis would definitely apply to it. If the time axis only applies to MW, Sonic’s world drops to 4-D, Cyberspace and the superdimensional spaces also drop to 5-D. Summing up:
Without R > F:
Cyberspace, Maginaryworld, superdimensional areas: 5-D
With R > F:
Arabian Nights: 3-D
Sonic and Blaze’s world: 4-D, possibly 5-D
Superdimensional spaces and Cyberspace: 5-D, possibly 6-D
Maginaryworld: 6-D