test: add Dockerized E2E test environment with Playwright + Mailpit (#860)

e2e/scripts/docker-entrypoint.sh

@@ -0,0 +1,36 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+echo "==> Waiting for worker at $WORKER_URL ..."
+for i in $(seq 1 60); do
+  if curl -sf "$WORKER_URL/health_check" > /dev/null 2>&1; then
+    echo "    Worker ready after ${i}s"
+    break
+  fi
+  if [ "$i" -eq 60 ]; then
+    echo "ERROR: Worker not ready after 60s"
+    exit 1
+  fi
+  sleep 1
+done
+
+echo "==> Waiting for frontend at $FRONTEND_URL ..."
+for i in $(seq 1 60); do
+  if curl -sf "$FRONTEND_URL" > /dev/null 2>&1; then
+    echo "    Frontend ready after ${i}s"
+    break
+  fi
+  if [ "$i" -eq 60 ]; then
+    echo "ERROR: Frontend not ready after 60s"
+    exit 1
+  fi
+  sleep 1
+done
+
+echo "==> Initializing database"
+curl -sf -X POST "$WORKER_URL/admin/db_initialize" > /dev/null
+curl -sf -X POST "$WORKER_URL/admin/db_migration" > /dev/null
+echo "    Database initialized"
+
+echo "==> Running Playwright tests"
+exec npx playwright test "$@"