feat: Add session status indicator and connection badge to UI

[Lalit7374]

Description

The GSoC 2026 roadmap includes "Session Management for Multiuser Support"
but currently the UI has zero visual indication of the current session
state, session ID, or WebSocket connection status.

Problem

• User has no way to know if they are connected to an active GDB session
• No session ID displayed — makes multiuser debugging impossible to track
• No visual indicator for "Connecting / Connected / Disconnected" states
• Lays no groundwork for the upcoming full multiuser session feature

Proposed Solution

• Add a small status bar or badge component in the header/navbar
• Display current connection state: Connecting... / Connected / Disconnected
• Generate and display a session UUID once a session is established
• Use color coding: green = connected, red = disconnected, yellow = connecting
• Store session ID in React state (foundation for future multiuser work)

Why This Matters

This is a small, scoped UI task that directly contributes to the
"Session Management for Multiuser Support" GSoC 2026 milestone.

I'd like to work on this

Can start with a focused PR this week.

[vrutank14t7]

Hi! I'm a MERN developer with hands-on experience in Socket.io (both backend and frontend) and real-time session management. I've built concurrent multiuser session handling in a production-level Rider/Driver app using Redis + BullMQ. I'd like to work on this issue and can submit a PR today. Is this still available to pick up?