[Feature] Support multiple files with tab interface

[kom50]

Summary

Allow users to work on multiple files within the same room.

Requirements

• Tab bar below header
• Add new file button (+)
• Rename file (double-click tab)
• Close file (x button on tab)
• Sync file changes across all users
• Each file has independent language mode
• Maximum 10 files per room

UI/UX

• Horizontal scrolling tab bar
• Active tab highlighted
• Unsaved indicator (dot) on tab
• Confirm dialog before closing

Data Structure

{
  roomId: "room-abc123",
  files: [
    { id: "file-1", name: "index.js", language: "javascript", content: "..." },
    { id: "file-2", name: "styles.css", language: "css", content: "..." }
  ],
  activeFile: "file-1"
}

Acceptance Criteria

• Users can create, rename, delete files
• Switching tabs shows correct content
• All users see file changes in real-time
• File state syncs for new users joining