Queen sheba is never described anywhere as being the ruler of hell, or actually the ruler of anything. If I had to guess, "queen" is an honorary title given to her for her witnessing the birth of hell, but there is no lore anywhere to support your claim that she actually rules anything. Similarly, nowhere in any of the DMC lore I know of is mundus ever described as "the only ruler of hell", only that he calls himself emperor and has many minions at his disposal.
Nowhere in the lore for either game does it say that demons are only visible from purgatory. But let's assume for the sake of your argument that you're actually right, can it still be explained?
Yes. Every demon in DMC is forced to manifest themselves in the human world through some physical medium that was already there. Sloths and wraths form sand to create bodies, other demons possess shadows, blood, bile, armor or even animals. You only ever see true demons when you are actually inside hell. It's entirely possible that demons don't interact with purgatory the same way angels do, which is why dante can be an effective demon slayer yet be ignorant of purgatory, and also why he never sees an angel.
"Eva, a truly extraordinary witch, entered into contract with a legendary dark knight, and then faced the amassed armies of Inferno." At this period, the entirety of hell was spilling into the human world; every human on the planet was fighting off demons. Are you saying that just because eva (a human witch) was fighting demons, there's no way sparda was also fighting demons? Once again, nowhere in DMC lore does it say that sparda fought hell alone. In fact, it seems to pretty heavily imply the exact opposite: that sparda fought hell with the backing of every human.
In DMC lore, the human world was described as a place that didn't always exist, and was formed from elsewhere. The DMC accounting of this event is that the human world was formed from a piece of hell itself. In Bayonetta, father balder confirms that the power to create a new human world is something the eyes of the world possess.
The trinities are created, the eyes of the world are used to create the human world, demons lay claim to the human world and say it was originally part of the demon world anyway. That was pretty easy.
TL;DR The bayonetta and DMC universes are both heavily based on
The Inferno, which should actually be pretty obvious.
Paradiso, purgatorio, inferno, and the human world caught up between the three? In DMC the main character 'Dante' is led by (chases) Vergil as he leads him through hell, they weren't exactly subtle about where they got their inspiration. The two universes are similar because they are both sourced from the same material, the only real difference is that DMC focuses heavily on inferno, ignoring paradiso and purgatorio, while bayonetta expands deeply on those two realms while being vague about inferno.
Looking at it from the perspective of the source material, it's extremely obvious that both stories were told to overlap as little as possible.