[FEATURE] Display current active model persistently in the UI

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

When using Claude Code, it's not always obvious which model (Opus, Sonnet, Haiku, etc.) is currently active — especially when switching models mid-session, or when a mode change (e.g. Fast mode) implicitly affects the model tier. Users have to run /model or check settings to confirm what they're talking to.

Proposed Solution

Show the current model persistently in the UI, similar to how "auto mode" or "plan mode" are already indicated inline during a session. Ideally a small always-visible badge/indicator (e.g. in the statusline or prompt area) showing the active model name, so the user can tell at a glance which model is active without running a command.

Alternative Solutions

Currently the model can be surfaced via a custom statusLine command, but this requires manual setup and isn't a built-in indicator.

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

1. I'm running a long session and switch models with /model or toggle Fast mode.
2. Without checking /model or settings, I can't tell which model is currently responding.
3. With a persistent indicator, I could glance at the prompt/statusline and immediately confirm the active model, the same way I can already tell auto mode or plan mode is active.

Additional Context

Similar in spirit to existing mode indicators (auto mode, plan mode) that are already shown inline during a session.