Add GitHub Actions workflow to build and push backend image

.github/workflows/backend-docker.yml

@@ -0,0 +1,52 @@
+name: Build and Push Backend Docker Image
+
+on:
+  push:
+    branches: [ "main" ]
+    paths:
+      - "parental-control-system/backend/**"
+      - ".github/workflows/backend-docker.yml"
+  workflow_dispatch:
+
+permissions:
+  contents: read
+  packages: write
+
+env:
+  IMAGE_NAME: ghcr.io/${{ github.repository_owner }}/parental-control-backend
+
+jobs:
+  docker:
+    runs-on: ubuntu-latest
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Set up Docker Buildx
+        uses: docker/setup-buildx-action@v3
+
+      - name: Log in to GHCR
+        uses: docker/login-action@v3
+        with:
+          registry: ghcr.io
+          username: ${{ github.actor }}
+          password: ${{ secrets.GITHUB_TOKEN }}
+
+      - name: Extract metadata (tags, labels)
+        id: meta
+        uses: docker/metadata-action@v5
+        with:
+          images: ${{ env.IMAGE_NAME }}
+          tags: |
+            type=sha
+            type=raw,value=latest
+
+      - name: Build and push
+        uses: docker/build-push-action@v6
+        with:
+          context: ./parental-control-system/backend
+          file: ./parental-control-system/backend/Dockerfile
+          push: true
+          tags: ${{ steps.meta.outputs.tags }}
+          labels: ${{ steps.meta.outputs.labels }}