As a general rule, a script that is thousand-lines-long and doing multiple things is bad, because it's hard to decouple things, it can lead to unrelated-things bugs and cause trouble if you are working in a team. If you can split functionality, it is better to have several scripts focusing on specific logic. Unless you are alone and you're comfortable with large files :p
But even alone, if you come back one month later you'll wonder, "where the hell did I implemented this thing? What the fuck is this script doing?"
In my game I have such a script, but this is because 75% of it is running inside
_fixed_process() for complex physics interaction, and it has debug code to monitor if everything is going well. At least, I managed to separate camera management on the camera node, because it's not related to physics and can work on its own. At the moment I have to keep the big script on the root node because it's a KinematicBody2D, I can't change it easily. If it becomes a problem, maybe I could create classes in separate files, instantiate them on the attached script, then forwarding events to them, actually reproducing a "component" approach, kind of. Or have child nodes, which is nice to have in the editor, but only if it makes sense from a designer point of view. If it's pure programmer logic, better have it hidden :p
If levels are big, you can load them (or parts of them) asynchronously: http://docs.godotengine.org/en/latest/tutorials/engine/background_loading.html
I only tested Windows 7, Windows 10 and Android export yet, they work well with no bugs at all. HTML5 is buggy, but sometimes kinda works. iOS is hard to test because I'd need a Mac. Apple is so annoying.
I'm developing a game myself, and I'm curious about possible approaches too so I don't have answer to everything. Experience in other engines/frameworks can help.
Edit: I see you added
globals to your tags. Avoid global states. As much as you can. Use the hierarchy, references, have everything in a scope. I use globals only for stateless static functions or nodes that will be there for the whole program execution, not just game and menu, so... not that much :p