cleanup: Remove unused StateContext from AppController.tsx

[coderabbitai]

Description

As noted in PR #224, we should clean up the AppController component since we no longer need the StateContext:

• Remove the creation of StateContext since it's no longer needed
• Remove the unused export of StateContext
• Replace the <StateContext.Provider value={null}> wrapper with a simple <div> wrapper in the AppController component
• Rename the interface StateContextProviderProps to AppControllerProps

This is a cleanup task after migrating from React Context to Zustand for state management.

References

• Discussion: refactor: Replace StateContextProvider with Zustand for state management (resolves #168, resolves #211). #224 (comment)
• Requested by: @junhaoliao