Update CI to push Docker images to ghcr.io (#35)

Enable image pushing to GitHub Container Registry on main branch
merges. Tags images with both commit SHA and latest.

Co-authored-by: Groom Book CTO <cto@groombook.app>
Co-authored-by: Paperclip <noreply@paperclip.ing>

.github/workflows/ci.yml

@@ -69,32 +69,46 @@ jobs:
         run: pnpm build
 
   docker:
-    name: Build Docker Images
+    name: Build & Push Docker Images
     runs-on: ubuntu-latest
     needs: [build]
     if: github.ref == 'refs/heads/main'
+    permissions:
+      contents: read
+      packages: write
     steps:
       - uses: actions/checkout@v4
 
       - name: Set up Docker Buildx
         uses: docker/setup-buildx-action@v3
 
-      - name: Build API image
+      - name: Log in to GitHub Container Registry
+        uses: docker/login-action@v3
+        with:
+          registry: ghcr.io
+          username: ${{ github.actor }}
+          password: ${{ secrets.GITHUB_TOKEN }}
+
+      - name: Build and push API image
         uses: docker/build-push-action@v6
         with:
           context: .
           file: apps/api/Dockerfile
-          push: false
-          tags: groombook/api:${{ github.sha }}
+          push: true
+          tags: |
+            ghcr.io/groombook/api:${{ github.sha }}
+            ghcr.io/groombook/api:latest
           cache-from: type=gha
           cache-to: type=gha,mode=max
 
-      - name: Build Web image
+      - name: Build and push Web image
         uses: docker/build-push-action@v6
         with:
           context: .
           file: apps/web/Dockerfile
-          push: false
-          tags: groombook/web:${{ github.sha }}
+          push: true
+          tags: |
+            ghcr.io/groombook/web:${{ github.sha }}
+            ghcr.io/groombook/web:latest
           cache-from: type=gha
           cache-to: type=gha,mode=max