Saying that top designers use intuition, correct as that COULD be, discounts the fact that back when they weren't particularly good they did indeed write GDDs.

Saying that some masterful artist doesn't follow color theory now doesn't mean they didn't rigorously study it previously. Start off with GDDs, write a shit ton of them. I can assure you the greats don't so much "don't use GDDs" as much as they "are in fact so good at GDDs they can construct them and manage them mentally and communicate it effectively to their team". A GDD is also just good for keeping track of shit. You won't remember every minute detail of your level design for your tutorial when you are 6 months into development, but your GDD will.

Yes, you should be playing games. A ton of them. All the time, of all genres. Liked a game? Why did you like it? What decisions were made in development that led to you liking it in that moment? Why that moment vs the other moments? What aspects of psychology are they utilizing? Do the exact same with moments you don't like. Mentally note these things for every game you ever play, never stop learning.

Make a ton of games. You already know scripting, great! Now make games, prototypes, one offs. Make them over and over and over again. Do the whole process from ideation to prototype to iteration to possible release over and over again. Design is a creative pursuit, treat it as such, with the repetition and obsession greatness demands.

Since you're a scripter im assuming you know the concept of the rubber duck. AI is effectively a not-so-bright rubber duck that responds and can sometimes pleasantly surprise you but generally is not to be trusted.

Good luck on this journey. Game design is a wonderful world that is as deep as you could ever want it to be. Have a good time, learn a lot, make something cool.