fix: wait for FastAPI/Next.js health before starting nginx

- Replace fixed sleep 5 with health-check loops (up to 120s for FastAPI,
60s for Next.js) so nginx only starts proxying once backends are ready
- Fix NEXT_PUBLIC_API_URL in Dockerfile to /api (relative) instead of
hardcoded localhost:8000

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Dockerfile

@@ -4,7 +4,8 @@ WORKDIR /app/frontend
 COPY frontend/package*.json ./
 RUN npm ci
 COPY frontend/ ./
-ENV NEXT_PUBLIC_API_URL=http://localhost:8000
+#ENV NEXT_PUBLIC_API_URL=http://localhost:8000
+ENV NEXT_PUBLIC_API_URL=/api
 RUN npm run build
 
 FROM python:3.11-slim

start.sh

@@ -19,7 +19,24 @@ npm run start -- --port 3000 &
 NEXTJS_PID=$!
 echo "Next.js started (PID $NEXTJS_PID)"
 
-sleep 5
+echo "Waiting for FastAPI to be ready..."
+for i in $(seq 1 120); do
+    if curl -sf http://localhost:8000/ > /dev/null 2>&1; then
+        echo "FastAPI is ready (${i}s)"
+        break
+    fi
+    sleep 1
+done
+
+echo "Waiting for Next.js to be ready..."
+for i in $(seq 1 60); do
+    if curl -sf http://localhost:3000/ > /dev/null 2>&1; then
+        echo "Next.js is ready (${i}s)"
+        break
+    fi
+    sleep 1
+done
+
 nginx -g "daemon off;" &
 
 NGINX_PID=$!