fix: ensure graceful shutdown in non-interactive chat mode

[avoidwork]

Description

The --chat mode was falling through after the conversation completes without calling the shutdown handler. This left the session unsaved, the GC manager running, and telemetry unflushed. Extracted the shutdown logic into a named runShutdown() function and call it explicitly before process.exit(0).

Type of Change

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Documentation update
• Refactor (no functional changes)
• Performance improvement
• CI / build / tooling

Testing

All existing tests pass. The change extracts existing shutdown logic into a named function (no new behavior introduced) and calls it in the --chat mode path. No new functions require new unit tests — the existing shutdown handler tests cover the extracted logic.

Coverage

• 100% line coverage maintained

Checklist

• npm run lint passes
• Tests pass with 100% line coverage
• No forbidden patterns used
• Conventional Commit style applied