Status line shows global default model instead of the actual model running in each thread

Bug Description

The status line model indicator reflects the global default model rather than the model actually being used in a given thread. This causes misleading display behavior when multiple threads are open.

Steps to Reproduce

1. Open two threads (Thread A and Thread B), both running Sonnet
2. In Thread A, run /model and switch to Haiku
3. Observe: Thread B's status line now shows "Haiku 4.5"
4. But Thread B is still actually running Sonnet (it started on Sonnet and was never switched)

Expected Behavior

The status line should show the model actually running in that thread, not the global default. Each thread should display its own active model independently.

Actual Behavior

When the default model is changed in one thread, all other open threads' status lines update to reflect the new default — even though those threads are still using their original model.

Environment

• Claude Code CLI
• macOS (darwin 24.6.0)