Statusline: rate limits are inaccurate and disappear

Description

Two issues with the statusline rate-limit display:

1. Limits shown on the statusline are not accurate

The rate-limit values displayed in the statusline do not reflect the actual current usage/remaining limits. The numbers appear stale or miscalculated, making it unreliable for users to gauge how much capacity they have left.

2. Limits on the statusline disappear

After some time or after certain interactions, the rate-limit information vanishes from the statusline entirely. The statusline remains visible but the limit indicators are gone, leaving no way to monitor usage without restarting the session.

Expected behavior

• Rate limits should accurately reflect current usage and remaining quota at all times.
• Limit indicators should persist on the statusline and update continuously throughout the session.

Environment

• codex version: 0.113.0
• OS: Linux (Arch Linux, x86_64)