[FEATURE] Show subagent model and config in subagent detail view

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When a subagent is spawned (e.g. via the Agent tool, or a custom subagent defined in .claude/agents/), drilling into its detail view in the Claude Code UI does not show which model it is running on. Teams that pin subagents to specific models — or set an org-wide floor via CLAUDE_CODE_SUBAGENT_MODEL — have no way to visually confirm, from inside a running session, which model a given subagent actually used. This forces guesswork or after-the-fact log/telemetry digging when debugging cost, latency, or quality differences between subagent runs.

Proposed Solution

Surface the subagent's resolved runtime configuration in the subagent detail view, including at minimum:

• Model name (the resolved model, after any CLAUDE_CODE_SUBAGENT_MODEL env floor or per-agent model: frontmatter is applied — not just the frontmatter value)
• Agent type / name (which subagent definition was invoked)
• Allowed tools for that subagent
• Reasoning effort, if applicable to the resolved model

This could be a small metadata header or expandable panel at the top of the subagent detail view, similar to how the main session header already shows the active model.

Alternative Solutions

Currently the only way to infer the model is to cross-reference OpenTelemetry spans (if telemetry is configured) or read .claude/agents/*.md frontmatter and manually apply any CLAUDE_CODE_SUBAGENT_MODEL override by hand — neither is visible in the UI itself, and neither confirms what actually happened at runtime.

Priority

High - Significant impact on productivity

Feature Category

Interactive mode (TUI)

Use Case Example

1. Our org sets CLAUDE_CODE_SUBAGENT_MODEL=sonnet in settings.json as a cost/quality floor, while individual developers pick their own main-loop model.
2. A subagent (e.g. test-engineer) is spawned mid-session to write Cypress specs.
3. I drill into that subagent's detail view to check whether it's behaving as expected.
4. With this feature, I could immediately see it resolved to Sonnet (confirming the env floor applied correctly) instead of having to guess or dig through telemetry.

Additional Context

Related setting: CLAUDE_CODE_SUBAGENT_MODEL (routes all subagents to a floor model regardless of per-agent model: frontmatter). Showing the resolved model in the detail view would make this override visibly verifiable per-run, not just documented behavior.