Restore PostHog session recording

[zahlekhan]

Summary

• load the full posthog-js browser package instead of the slim module
• re-enable PostHog session recording with a 10% sample rate
• allow the recorder extension to load by removing disable_external_dependency_loading

Root cause

The deferred analytics refactor switched the site to posthog-js/dist/module.slim and explicitly disabled both external dependency loading and session recording. That configuration continued to capture pageviews but prevented the session recorder from loading.

Impact

OpenUI site sessions can be recorded again at the previous 10% sampling rate while retaining deferred PostHog initialization.

Validation

• pnpm install --frozen-lockfile
• pnpm --filter @openuidev/docs exec prettier --check lib/analytics.ts
• pnpm --filter @openuidev/docs exec eslint lib/analytics.ts
• pnpm --filter @openuidev/docs types:check
• git diff --check

The production docs build was also attempted, but Next.js/Turbopack remained at Creating an optimized production build ... without further output for several minutes, so it was stopped and is reported as inconclusive rather than passing.