Implement PostHog monitoring for Next apps

[anth-volk]

Fixes #921

Summary

• add PostHog bootstrap to the Next website and calculator-app apps
• proxy PostHog traffic through app-local /_euclid rewrites and add shared client/server helpers
• add website interaction tracking for the hero CTA, newsletter flow, country switching, and research pages
• add calculator tracking for report-builder selections, report creation, household flows, calculation lifecycle, and report-output views
• add Next and shared React error capture for both apps
• add env examples plus standard Node 24 version files for local/dev consistency

Validation

• bun install
• cd app && bun run typecheck
• cd website && bun run typecheck
• cd calculator-app && bun run typecheck
• cd website && bun run build
• cd calculator-app && bun run build
• manual smoke tests for the website hero CTA event and calculator report-builder events

Notes

• this PR focuses on bootstrap, core events, proxying, and error capture
• replay enablement and source-map/release upload are still follow-up work

[vercel]

The latest updates on your projects. Learn more about Vercel for GitHub.

Project	Deployment	Actions	Updated (UTC)
policyengine-app-v2	Ready	Preview, Comment	Apr 6, 2026 5:28pm
policyengine-calculator	Ready	Preview, Comment	Apr 6, 2026 5:28pm
policyengine-calculator-next	Ready	Preview, Comment	Apr 6, 2026 5:28pm
policyengine-website	Ready	Preview, Comment	Apr 6, 2026 5:28pm