Status line shows wrong model when multiple instances are running with different models

When multiple Claude Code instances are open simultaneously, the status line model display can show the wrong model. Specifically, if Instance A changes to a non-default model, Instance B's status bar begins showing Instance A's model instead of its own.

Instance B's status bar will only correct itself if its model is explicitly changed away from the default.

This suggests the model field in the status line input data is sourced from a shared/global location rather than being tracked per-session.

Steps to reproduce

1. Open two instances of Claude Code (both using the default model, Opus 4.6)
2. In Instance A, switch to a non-default model (e.g., /model sonnet)
3. Observe Instance B's status bar — it now shows Sonnet instead of Opus

Expected

Each instance's status bar reflects its own active model

Actual

Instance B's status bar reflects Instance A's model change

Version

2.1.45