Copy release images to prod ECR (#8101)

## Problem
We want to have all released images in production ECR repository

## Summary of changes
Copy all docker images to production ECR repository

cc: https://github.com/neondatabase/cloud/issues/10177

.github/workflows/build_and_test.yml

@@ -1070,7 +1070,8 @@ jobs:
           username: ${{ secrets.NEON_DOCKERHUB_USERNAME }}
           password: ${{ secrets.NEON_DOCKERHUB_PASSWORD }}
 
-      - uses: docker/login-action@v3
+      - name: Login to dev ECR
+        uses: docker/login-action@v3
         with:
           registry: 369495373322.dkr.ecr.eu-central-1.amazonaws.com
           username: ${{ secrets.AWS_ACCESS_KEY_DEV }}
@@ -1104,6 +1105,22 @@ jobs:
           docker buildx imagetools create -t neondatabase/neon-test-extensions-v16:latest \
                                              neondatabase/neon-test-extensions-v16:${{ needs.tag.outputs.build-tag }}
 
+      - name: Login to prod ECR
+        uses: docker/login-action@v3
+        if: github.ref_name == 'release'|| github.ref_name == 'release-proxy'
+        with:
+          registry: 093970136003.dkr.ecr.eu-central-1.amazonaws.com
+          username: ${{ secrets.PROD_GHA_RUNNER_LIMITED_AWS_ACCESS_KEY_ID }}
+          password: ${{ secrets.PROD_GHA_RUNNER_LIMITED_AWS_SECRET_ACCESS_KEY }}
+
+      - name: Copy all images to prod ECR
+        if: github.ref_name == 'release'|| github.ref_name == 'release-proxy'
+        run: |
+          for image in neon compute-tools {vm-,}compute-node-{v14,v15,v16}; do
+            docker buildx imagetools create -t 093970136003.dkr.ecr.eu-central-1.amazonaws.com/${image}:${{ needs.tag.outputs.build-tag }} \
+                                               369495373322.dkr.ecr.eu-central-1.amazonaws.com/${image}:${{ needs.tag.outputs.build-tag }}
+          done
+
   trigger-custom-extensions-build-and-wait:
     needs: [ check-permissions, tag ]
     runs-on: ubuntu-22.04