[integrations] entity-extraction-worker: fix fence parsing + misleading provider error

[eazene]

What

Two production bugs in the entity-extraction worker that together created invisible poison-pill queue items.

The bugs

1. Anchored fence regex misses real LLM output. stripCodeFences used /^\``(?:json)?\s*\n?([\s\S]?)\n?\s```$/— anchored at both ends. A```jsonfence with trailing prose after the close, or an unterminated fence, falls through toJSON.parse` and throws. It's content-dependent: thoughts about formatting rules nudge the model into markdown mode, so the same queue items failed on every retry (to dead-letter) while 270+ others succeeded.

2. Misleading fall-through error. When every configured provider fails transiently, extractEntities threw 'No LLM API key configured' — even though keys were configured and the real failure was the parse error above. That masking survived four separate debugging attempts; the real cause was only visible after making the error honest.

The fix

• Fence stripper: try the anchored match first; if it misses but the text starts with a fence, strip the opening fence and cut at the next closing fence (both index.ts and _shared/helpers.ts).
• Track lastProviderError through the provider chain; the fall-through now throws 'All configured LLM providers failed — last error: …' and reserves the no-key message for when no key is actually set.

Verification (live)

Deployed against a production queue: the honest error immediately revealed the fence bug; after the fence fix, the stuck item (4/5 attempts, one retry from permanent failed) parsed and completed. Queue went to 279/279 complete.

🤖 Generated with Claude Code

[github-actions]

OB1 PR Gate

✅ Folder structure — All files are in allowed directories
✅ Required files — README.md and metadata.json found in all contribution folders
✅ Metadata valid — All metadata.json files passed JSON Schema validation
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✅ Contribution dependencies — All declared skill and primitive dependencies exist and are linked in README
✅ LLM clarity review — Covered by Claude PR Review workflow
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✅ Tool audit link — Extensions/integrations link to the MCP Tool Audit guide
✅ Scope check — All changes are within the contribution folder(s)
✅ Internal links — All relative links in READMEs resolve to existing files

Result: All 15 checks passed! Ready for human review.

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Post-Merge Tasks

These don't block merge — they're reminders for admins after this PR lands.

• Add Entity Extraction Worker to integrations/README.md
• Add Alan Shurafa (@alanshurafa) to CONTRIBUTORS.md
• Post in OB1 Discord #show-and-tell