I think you can add a metatable to _G with an __index function. This should be called when accessing undefined local variables (as they end up trying to access the global scope _G) and you can thrown an error.
You can. In our game engine ~10 years ago we would hook the global table to stop designers from creating globals (the default in Lua without using the local keyword) at certain areas in the game frame, mostly to stop this exact trap.
I toyed with the idea of inverting the semantics of global and local in lua and to remove "local" and instead default to local and have a "global" keyword. Looking at lua.c quickly dissuaded me when I was a much more junior programmer, but now days it might be fun to try.
Local by default would have been a much better choice. The entirety of my code looks like local this local that. In all my years of Lua I have only found 1 reason to use a global variable: in Love2D when loading a texture, a local variable will go out of scope and get garbage collected, resulting in a black texture, but a global variable will not. Maybe it's even been fixed by now, as that was years ago.
Yes, you can control a namespace (in the form of a table, of course) in which a module you require executes. The global definitions are then placed in the table. You can implement copy-on-write using this namespace and a metatable, you can change the semantics of accessing an uninitialized (global) variable, etc. Lua is incredibly flexible, after all. Unfortunately, since you have to implement (and then maintain!) those yourself, it's hard to justify (IME) using Lua instead of a more full-featured solution (that might still incorporate Lua somewhere in the stack[0]), esp. since the main selling point of Lua is simplicity.
[0] You can use something like Fennel or Haxe to compile a more structured language to Lua, or you can use an alternative implementation like Luau.
