[Frontend]: Add chat session lifecycle and recovery UX

[Hanseooo]

Problem

Current backend session storage is in-memory, so sessions can disappear on backend restart. Frontend needs resilient session lifecycle handling.

Scope

• Persist session_id in client state/storage.
• Attempt session restore via GET /api/chat/{session_id}.
• Handle session-not-found/expired cases with clear recovery UX.
• Add explicit "Start new plan" / reset conversation action.

Acceptance Criteria

• Session resumes when available.
• If session is missing, user gets a clear recovery path (no dead-end states).
• Reset action starts a clean planning flow.

Priority

Stability

Dependencies

• Depends on: [Frontend]: Implement chat API client and React Query hooks #25
• Blocks: reliable multi-step usage across page refreshes/restarts