Playground: file browser to save/load student code

[yvanvds]

In "vrij coderen" / playground mode, students currently have no way to save and reload their code. We need a simple file browser so students can:

• save the current buffer under a name
• list their saved files
• open one to continue working

Scope question to settle before implementing: local-only, or synced to the student's Azure account so it follows them across devices?

Moved from TODO.md "future ideas".