Add analytics on AI chat

[zenoachtig]

Summary

• track ask_question when posting to AI chat

Testing

• bun format packages/gitbook/src/components/AI/useAIChat.tsx
• bun format:check (fails: diagnostics exceed limit)
• bun run unit (fails: unable to access external URLs)
• bun run build (fails: failed to fetch fonts from Google)
• bun run typecheck

---

https://chatgpt.com/codex/tasks/task_b_686245ce70b4832bb5c2e06c22de5fc4

[changeset-bot]

⚠️ No Changeset found

Latest commit: e526eb0

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

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[github-actions]

Summary of the deployments:

Version	URL	Status
Vercel	https://gitbook-v2-4xeajgs1h-gitbook.vercel.app	✅
Cloudflare	https://12241041-gitbook-open-v2-preview.gitbook.workers.dev	✅

Test content

Site	2v	2c
GitBook	https://gitbook-v2-4xeajgs1h-gitbook.vercel.app/url/gitbook.com/docs	https://12241041-gitbook-open-v2-preview.gitbook.workers.dev/url/gitbook.com/docs
E2E	https://gitbook-v2-4xeajgs1h-gitbook.vercel.app/url/gitbook.gitbook.io/test-gitbook-open	https://12241041-gitbook-open-v2-preview.gitbook.workers.dev/url/gitbook.gitbook.io/test-gitbook-open

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Build	Status	Details	Updated (UTC)
customers-v2 (Inspect)	👍 Changes approved	80 changed	Jun 30, 2025, 8:27 AM
v2-cloudflare (Inspect)	👍 Changes approved	3 changed	Jun 30, 2025, 8:30 AM
v2-vercel (Inspect)	👍 Changes approved	5 changed	Jun 30, 2025, 8:29 AM