Always show which agent/model is currently active

### Feature summary

Always show which agent/model is currently active in the session.

### What problem are you trying to solve?

There is no on-screen indicator of which agent (or model) is active in the current session. I can't tell at a glance what I'm talking to, which makes it easy to send a message to the wrong agent or misjudge a response.

### Proposed solution

Always display the active agent/model name in the UI (e.g. a persistent label in the session header or input bar). Update it immediately when the agent/model changes, and ideally make it clickable to switch.

### Workflow impact

Removes guesswork, prevents sending messages to the wrong agent, and makes multi-agent / multi-model use clearer and faster.

### Installation context

GitHub Copilot desktop app on macOS (personal machine).

### Additional context

Today nothing on the main screen shows the current agent. A small always-visible indicator would be enough.