feat(workflow): add GitHub Actions workflow for building and pushing Docker image

.github/workflows/docker-build.yml

@@ -0,0 +1,61 @@
+name: Build and Push Docker Image
+
+on:
+    push:
+        branches:
+            - master
+        paths:
+            - "package.json"
+            - "Dockerfile"
+            - ".github/workflows/docker-build.yml"
+
+jobs:
+    build:
+        runs-on: ubuntu-latest
+
+        permissions:
+            contents: read
+            packages: write
+
+        steps:
+            - name: Checkout code
+              uses: actions/checkout@v6
+
+            - name: Set up Docker Buildx
+              uses: docker/setup-buildx-action@v3
+
+            - name: Login to Docker Hub
+              uses: docker/login-action@v4
+              with:
+                  username: ${{ secrets.DOCKERHUB_USERNAME }}
+                  password: ${{ secrets.DOCKERHUB_TOKEN }}
+
+            - name: Login to GitHub Container Registry
+              uses: docker/login-action@v4
+              with:
+                  registry: ghcr.io
+                  username: ${{ github.actor }}
+                  password: ${{ secrets.GHCR_TOKEN }}
+
+            - name: Extract metadata
+              id: meta
+              uses: docker/metadata-action@v5
+              with:
+                  images: |
+                      docker.io/${{ secrets.DOCKERHUB_USERNAME }}/website
+                      ghcr.io/${{ github.repository }}
+                  tags: |
+                      type=ref,event=branch
+                      type=semver,pattern={{version}}
+                      type=sha
+                      type=raw,value=latest
+
+            - name: Build and push
+              uses: docker/build-push-action@v6
+              with:
+                  context: .
+                  push: true
+                  tags: ${{ steps.meta.outputs.tags }}
+                  labels: ${{ steps.meta.outputs.labels }}
+                  cache-from: type=gha
+                  cache-to: type=gha,mode=max