[BUG] Switching models does not update context infos immediately

[JosXa]

1. Have a conversation with a small-context model.
2. During idle, switch models to a large one (e.g. Gemini 3 Pro)
3. The context info in the top right does not update:

You have to send a message for it to update.

If I want to just see it apply or how much context that other model would have left, I can't.

[github-actions[bot]]

This issue might be a duplicate of existing issues. Please check:

• #5760: Context size in sidebar not updated after /compact - Similar issue where sidebar context info is stale and only updates after sending a new message