[FEATURE] Show current model name in the CLI status bar

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

It's easy for the active model to get switched in one tab while multitasking across several, without anyone noticing. Since the status bar shows mode, shortcuts, and effort but no model name, the switch goes unnoticed until usage limits are already burned on a model that wasn't meant to be used.

Proposed Solution

Add the model name to the existing status bar, next to the other indicators. Update it live whenever the model changes, so a switch is caught immediately instead of discovered after the fact.

Alternative Solutions

None really; the only current option is running a separate command to check, which doesn't help if no one's actively looking.

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

Working across multiple tabs, one tab quietly switches to a different model. Work continues as normal, and the mistake is only caught later when usage is checked and the limit is gone on a model that wasn't intended to run.

Additional Context

<img width="1568" height="172" alt="Image" src="https://github.com/user-attachments/assets/483e8a14-e8e5-45fb-8f67-e3691691b5d9" />