feat: setup PostHog analytics for client and server

Summary

Imported from GitHub PR #40.

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  "repo": "The-Connell-School/yawp-2.0",
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  "state": "MERGED",
  "title": "feat: setup PostHog analytics for client and server",
  "branch": "claude/issue-34-20250802-2046",
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  "number": 40,
  "syncedAt": "2026-05-26T21:38:23.523Z",
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