Bubble doesn't let you export code, right?

Right, not the HTML/JS. But Bubble does let you export a .bubble file (pages, elements, styles) and your data. We start there, and rebuild a real codebase, a real software with code that can be changed by a developer or an AI, like claude code, 
For the database, it's a little more complicated but we have build a tool for that. It will ensure that you really download all your data and from computer, without using our server).