[BUG] statusLine.refreshInterval ignored in VS Code extension — script never re-invoked on interval

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

statusLine.refreshInterval is configured to 60 seconds but the statusline script
is never called on that interval. The displayed values (e.g. rate-limit countdown)
freeze at the last event-triggered run and only refresh when a new assistant
response arrives.

Verified by adding a timestamp log to the script:
echo "$(date +%T)" >> /tmp/statusline-debug.log

After leaving the session idle for several minutes, no new entries appear in the log.

What Should Happen?

The script should be re-invoked every 60 seconds regardless of user activity,
as documented — keeping time-based segments current during idle periods.

Error Messages/Logs

Steps to Reproduce

1. Configure statusLine with refreshInterval in settings.json:

     {
       "statusLine": {
         "type": "command",
         "command": "bash ~/.claude/statusline.sh",
         "refreshInterval": 60
       }
     }

1. Add a timestamp log at the top of the statusline script:

echo "$(date +%T)" >> /tmp/statusline-debug.log

1. Start a session in the VS Code extension (useTerminal: false), send one message.

1. Leave the session idle for 3+ minutes without interaction.

1. Inspect the log: only one entry appears (the initial event trigger).

No subsequent entries are added by the interval.

Additional Information
Related: #77829 (statusLine not rendered in VS Code panel — broader surface gap).

Note: rate_limits fields are also absent from the input JSON on refresh runs
(resets_at is always empty), consistent with #95918. The refreshInterval issue
is independent: even if rate_limits were populated, the script is never called.

Claude Model

Not sure / Multiple models

Is this a regression?

I don't know

Last Working Version

_No response_

Claude Code Version

2.1.80

Platform

Anthropic API

Operating System

macOS

Terminal/Shell

VS Code integrated terminal

Additional Information

_No response_