Modify Docker build workflow for private registry

Updated the workflow to include login to a private Docker registry and changed the image tags for pushing.

.github/workflows/docker-build.yml

@@ -1,4 +1,4 @@
-name: Build Astro Image
+name: Build and Push Astro Image
 
 on:
   push:
@@ -19,19 +19,18 @@ jobs:
         id: vars
         run: echo "sha_short=$(git rev-parse --short HEAD)" >> $GITHUB_OUTPUT
 
-      - name: Build and Export to Docker
+      - name: Login to Private Registry
+        uses: docker/login-action@v3
+        with:
+          registry: docker-ui.illegalesachen.download
+          username: ${{ secrets.DOCKER_USERNAME }}
+          password: ${{ secrets.DOCKER_PASSWORD }}
+
+      - name: Build and Push
         uses: docker/build-push-action@v5
         with:
           context: .
-          load: false 
+          push: true
           tags: |
-            astro:latest
-            astro:${{ steps.vars.outputs.sha_short }}
-          outputs: type=docker,dest=/tmp/astro-image.tar
-
-      - name: Upload Artifact
-        uses: actions/upload-artifact@v4
-        with:
-          name: astro-docker-${{ steps.vars.outputs.sha_short }}
-          path: /tmp/astro-image.tar
-          retention-days: 7
+            docker-ui.illegalesachen.download/repository/astro-homepage:latest
+            docker-ui.illegalesachen.download/repository/astro-homepage:${{ steps.vars.outputs.sha_short }}