Status line doesn't reflect subagent model overrides; shows wrong subscription tier

Description

Two related display issues with the status line shown above "Auto Mode" in the Claude Code CLI:

1. Subagent model not reflected: When dispatching a subagent via the Agent tool with an explicit model override (e.g. requesting fable for a background planning task while the main interactive session runs on sonnet), the status line continues to show the main session's model. There's no visual indication of which model a running background subagent is actually using.

1. Incorrect subscription tier shown: The status line displays "Claude Pro" even though the account is on a Claude Max plan.

Expected behavior

• Ideally the status line (or another visible indicator) would reflect which model an active background subagent/task is running under, so it's clear when a delegated task (e.g. via /efficient-frontier-style orchestration) is actually using the requested frontier model vs. falling back to something else.
• The subscription tier shown should match the account's actual plan (Max, not Pro).

Context

Raised by a user during a session where a background planning subagent was explicitly dispatched with model: "fable"; the user had no way to confirm from the UI that the subagent was actually using that model, since the visible status line only ever reflects the top-level interactive session.

_Filed on behalf of the user via their Claude Code session._