[Feature] UI panel in /chat for users to configure personal context (state.pi)

[sami-marreed]

What you want and why

Users should be able to configure personal information / context directly from the /chat UI — things like member IDs, location coordinates, preferences, or any free-form key-value pairs — without needing access to environment variables or server configuration.

This context is stored in state.pi (personal information field on AgentState) and is automatically injected into every LLM call as a ## User Context block appended to the first user message. Right now this field can only be set programmatically (e.g. CUGA_DEMO_MODE=health injects a hardcoded HEALTH_USER_CONTEXT). There is no way for an end user to set or update it through the UI.

How it could work

• Add a "Personal Context" settings panel accessible from the /chat page (e.g. via a user profile icon or a settings drawer).
• The panel allows users to input free-form text (or structured key-value pairs) that represents their personal context — e.g.:

  Member ID: 121231234
  Location: latitude 40.7128, longitude -74.0060
  Preferred language: English
  

• On save, the value is persisted (localStorage or a backend /api/user/context endpoint) and sent with each chat request so the server can populate state.pi.
• The server's event_stream reads the provided context into local_state.pi (same injection point already used for the health demo today).
• The field should be editable at any time; changes take effect from the next message.
• When state.pi is already set by a server-side mechanism (e.g. CUGA_DEMO_MODE=health), the server-side value should take precedence (or the UI should show it as read-only / pre-filled).

Links or extra context

• state.pi injection in the graph: src/cuga/backend/cuga_graph/nodes/cuga_lite/cuga_lite_graph.py — lines ~844–890 (appended as ## User Context to the first user message).
• Current server-side injection point: src/cuga/backend/server/main.py event_stream function — sets local_state.pi from HEALTH_USER_CONTEXT when CUGA_DEMO_MODE=health.
• SDK path: src/cuga/sdk.py — user_context parameter already accepted in invoke() and mapped to state.pi.
• The chat request handler in main.py would need to accept a user_context field from the frontend payload and pass it through to the existing local_state.pi assignment.