Oh man, a 200-page visual novel script in Google Docs? You are a braver soul than I am! 😂 I totally feel your pain on the formatting wars. There is nothing more demoralizing than spending 30 minutes fixing indents that Apple Books decided to "optimize" for you when you just wanted to do a quick proofread.
To answer your question directly yes, it has built-in cloud sync! It connects to Google Drive and iCloud depending on what device you are using. I literally just upload my .epub file to Drive on my PC, open the app on my tablet, and it's there instantly. No USB cables, no emailing drafts to myself, no juggling versions. It automatically remembers where I left off too, which is a lifesaver when I switch from my tablet to my phone during my commute.
Since you mentioned you are using Godot, I'm curious are you writing your script directly in a text editor and importing it, or are you using a dedicated narrative tool (like Twine or Ink) and exporting from there? I've been toying with integrating my EPUB drafts back into my engine, so I'd love to hear how you handle that pipeline.
If you do give it a shot this weekend, definitely let me know how it handles your VN script. I'm particularly curious how it manages the visual novel-specific formatting (like character names centered above dialogue, scene transitions, etc.). Worst case, you have a clean reading copy to catch typos—best case, you save hours of formatting headaches!
Good luck with the 200-pager! What genre is your VN, by the way?