[Bug] Terminal UI displays incorrect model name when subagents launch or switch models

Describe the bug
When a subagent is launched, the actual underlying model works properly, but the terminal interface displays the incorrect model name. This mislabeling occurs when explicitly suggesting a different model or when an automatic model switch takes place.

Steps to Reproduce

Launch a subagent task inside Claude Code.

Pass an explicit model override or trigger an automatic model change.

Observe the model name reported in the terminal output.

Expected Behavior
The terminal UI should accurately reflect the active model name being used by the running subagent.

Actual Behavior
The subagent executes with the correct model, but the terminal UI displays an incorrect model label/name.

Environment Info

Platform: Linux

Terminal/Host: VS Code

Version: 2.1.267

Feedback ID: db47aa24-ba3a-49cc-8dea-36ff22851782

Errors
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Reproduce the issue in Claude Code 2.1.267 on Linux through VS Code, using both an explicit subagent model override and an automatic model switch. Trace how the terminal UI obtains the model label during subagent launch and switching. Done means the terminal consistently displays the active underlying model in both cases, with regression coverage for each path.

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