Integrate datadog to backend for traces and logs (#1299)

Issue #1217 

**Key changes:**

- Add ddtrace library
- Wrap application to datadog serverless-init to collect traces and logs

.github/workflows/gcp_backend.yml

@@ -62,7 +62,7 @@ jobs:
         uses: docker/build-push-action@v6
         with:
           context: .
-          file: ./backend/Dockerfile
+          file: ./backend/Dockerfile.datadog
           push: true
           tags: gcr.io/${{ vars.GCP_PROJECT_ID }}/${{ env.SERVICE }}:latest
           cache-from: type=registry,ref=gcr.io/${{ vars.GCP_PROJECT_ID }}/${{ env.SERVICE }}:buildcache

backend/Dockerfile.datadog

@@ -0,0 +1,23 @@
+FROM python:3.11 AS builder
+
+ENV PATH="/opt/venv/bin:$PATH"
+RUN python -m venv /opt/venv
+
+COPY backend/requirements.txt /tmp/requirements.txt
+RUN pip install --no-cache-dir --upgrade -r /tmp/requirements.txt
+
+FROM python:3.11-slim
+
+WORKDIR /app
+ENV PATH="/opt/venv/bin:$PATH"
+
+RUN apt-get update && apt-get -y install ffmpeg curl unzip && rm -rf /var/lib/apt/lists/* && \
+    pip install --target /dd_tracer/python/ ddtrace
+
+COPY --from=builder /opt/venv /opt/venv
+COPY --from=gcr.io/datadoghq/serverless-init:1 /datadog-init /app/datadog-init
+COPY backend/ .
+
+EXPOSE 8080
+ENTRYPOINT ["/app/datadog-init"]
+CMD ["/dd_tracer/python/bin/ddtrace-run", "uvicorn", "main:app", "--host", "0.0.0.0", "--port", "8080"]