feat: add PostHog, move Plausible to v4, and drop Sentry session replay

PostHog loads after the page is idle through a same-origin /ingest proxy and follows the signed-in Convex user. Plausible uses the per-site script through a /pa proxy. Sentry keeps errors and traces only. Pages load only the @spoon/ui modules they import, and client code reads public env from publicEnv.ts so zod stays out of the browser. Both analytics integrations stay off until their env is set in Infisical prod.

docs/compose.prod.yml

@@ -38,7 +38,9 @@ services:
       - SENTRY_AUTH_TOKEN=${SENTRY_AUTH_TOKEN}
       - NEXT_PUBLIC_SITE_URL=${NEXT_PUBLIC_SITE_URL:-http://localhost:${NEXT_PORT:-3000}}
       - NEXT_PUBLIC_CONVEX_URL=${NEXT_PUBLIC_CONVEX_URL:-http://${BACKEND_CONTAINER_NAME:-spoon-backend}:${BACKEND_PORT:-3210}}
-      - NEXT_PUBLIC_PLAUSIBLE_URL=${NEXT_PUBLIC_PLAUSIBLE_URL:-https://plausible.gbrown.org}
+      - NEXT_PUBLIC_PLAUSIBLE_SRC=${NEXT_PUBLIC_PLAUSIBLE_SRC:-}
+      - NEXT_PUBLIC_POSTHOG_KEY=${NEXT_PUBLIC_POSTHOG_KEY:-}
+      - NEXT_PUBLIC_POSTHOG_HOST=${NEXT_PUBLIC_POSTHOG_HOST:-}
       - NEXT_PUBLIC_SENTRY_DSN=${NEXT_PUBLIC_SENTRY_DSN}
       - NEXT_PUBLIC_SENTRY_URL=${NEXT_PUBLIC_SENTRY_URL}
       - NEXT_PUBLIC_SENTRY_ORG=${NEXT_PUBLIC_SENTRY_ORG:-sentry}