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.

No files, tests, or entry points are identified in the issue. Start by locating the session header or input bar in the desktop UI, then trace how the active agent/model changes; the work is done when the current name remains visible and updates immediately after a change.

Written by the indexing model from the issue text.