Yeah, higher fps in the menu is expected, there is no logic running behind the scenes there, and only one character in view, and only one light, instead of 2 or 3
I think the demo experience is going to be pretty much as good as it will get, ultimately. To go a bit more in detail: Here I'm depending on the game engine itself (Godot) and how it runs on various hardware (it's like Unity, basically, and I have no control over it and its rendering performance). There are some things also in the game that probably demand more graphics power (they are a result of high customizability), which are this way by design and not 'fixable' (they increase the number of draw calls, making graphics more expensive to render). I'm sorry there's no better news to give. But I hope that the demo level performance will allow you to still enjoy the game, even if maybe not all the arenas.