Background agent permission requests - identify which agent

### Describe the feature or problem you'd like to solve

When a background agent requests a permission, it would be useful to know which background agent is requesting the permission. Identifying the agent in the request would be great.

### Proposed solution

When running a session with multiple background agents or fleet mode working in parallel, knowing which agent is requesting permission would be useful, especially if you use the option for "No, and tell co-pilot what to do instead". This will allow better control of the agents.

### Example prompts or workflows

"Please migrate the 3 repos from .NET 8 to .NET 10 using parallel background agents. Create a PR when done."

### Additional context

_No response_

The issue names no files, tests, or entry points. Start by tracing how the CLI presents background-agent permission requests and determine whether the requesting agent's identity is available there; done means parallel-agent requests can be distinguished, including when responding with instructions.

Written by the indexing model from the issue text.