Just a few thoughts, but maybe they’ll work on your inspiration (I do just wanna say I have no background in this whatsoever either but y’know, I like to think along lmao)
What if, instead of a menu on a screen, you thought about some in-world items that could technically help do the things you wanna do?
Take the map, for example. Technically, it works as a way to travel, but you’ve used an in-world visual.
With that same logic, you could look at other things as well. What about using a notebook to track stats? Or a photo album?
Especially for menus you call on temporarily, you can go quite a bit creative on design
Screens that stay as an overlay can get a little more tricky, as you’ll have to take the amount of place they use into consideration, giving the option to hide those screens can help, though.
Imagine having a piece of paper (or, again, a notebook) with notes written on them at the top-ish right. You could make it so players can hide it, and it just slides to the side in such a way that it’s easily called upon again, but doesn’t use too much of the screen. (Basically, like showing some tabs which, in-world, could be bookmarkers sitting between pages)
A style like you have right there (black background, blue line) could work, but perhaps in a different setting, it feels like a more futuristic one, a digital world, A city of neon.
And that’s another way to look at it, if your game happens in nature, you could take leaves and such as inspiration, lots of greens, beautiful colorful flowers, the shades of orange from autumn leaves.
As for your follow up question
It completely depends on your design, I’d say. If it’s like a bar containing time of day and such, I’d keep it (i.e. you might want to double check if it’s evening of still afternoon before you go somewhere)
If you already have a design you can somewhat hide. there’s no reason to take that away either
But if it’s a permanent screen which would otherwise take place away from what you want to show on your map, I’d hide it.
As for the button to close the map, you could either use the same button, which you used to open the map, again or put a clear closing X somewhere (or both)
Just try to be consistent, if everything closes on X and one menu suddenly only closes if you press the open button again, it’ll get confusing