Agents window: make model provider & billing clear for 3rd-party agents (Claude / Codex)

### Summary
Offering Claude and Codex in the agent dropdown is currently ambiguous: users can't tell which model provider or subscription the harness runs against. This has been strong, recurring feedback, and I couldn't get a single user to understand the value prop and how it actually works without a lengthy explainer.

### Main blocker: Which provider/subscription is being used?
Most users assume that picking Claude runs against **their own Claude Code subscription**, and they'd love to keep using it inside our Agents UI. In reality the harness routes through the Copilot proxy and **counts against their GitHub Copilot tokens**.

**Impact:** Users don't realize this isn't their existing Claude Code subscription and instead consumes Copilot tokens — a serious trust risk once they find out.

### Model picker vs. agent picker
Developers use the same umbrella terms ("Claude", "Codex") for both **model families** and the **harness products**. The model picker and the agent picker don't differentiate their intent enough, so it's unclear what a selection actually means.

**Impact:** Users don't understand the agent picker and avoid using it.

### Prior art
The Claude tooltip in the **editor window** is a nice pattern worth building on.

### Ideas (not committed)
- Improve the labels and hover/tooltip details in the Agents window to explain the provider/subscription and billing.
- Extend the editor-window Claude tooltip to the **Codex** harness.
- Add equivalent tooltips in the **Agents window**.
- A one-off explainer the first time a user picks a 3rd-party agent.
- Make the active subscription explicit, with an easy toggle (e.g. disabling the Copilot proxy for Claude — foundation already started).

/cc @TylerLeonhardt @giuspepe