Fix live stop errors and status display

[shaypal5]

Summary

• cast stopped_at updates for Postgres so stopping live mode does not throw a Worker exception
• validate live conversation status before requiring storage for cleaner 400s
• prevent raw HTML error pages from being rendered in the dashboard status line

Verification

• npm run check
• npm run test
• npm run build
• manually exercised the operator live stop endpoint against the live database; session live_a42071f5f11c49898f returned 200 and status stopped