add pooler step to ghcr workflow

.github/workflows/publish_ghcr_image.yaml

@@ -3,6 +3,7 @@ name: Publish multiarch postgres-operator images on ghcr.io
 env:
   REGISTRY: ghcr.io
   IMAGE_NAME: ${{ github.repository }}
+  IMAGE_NAME_POOLER: ${{ github.repository }}-pooler
   IMAGE_NAME_UI: ${{ github.repository }}-ui
 
 on:
@@ -34,6 +35,12 @@ jobs:
             OPERATOR_IMAGE="${{ env.REGISTRY }}/${{ env.IMAGE_NAME }}:${GITHUB_REF/refs\/tags\//}"
             echo "OPERATOR_IMAGE=$OPERATOR_IMAGE" >> $GITHUB_OUTPUT
 
+      - name: Define pooler image name
+        id: image_pooler
+        run: |
+            POOLER_IMAGE="${{ env.REGISTRY }}/${{ env.IMAGE_NAME_POOLER }}:${GITHUB_REF/refs\/tags\//}"
+            echo "POOLER_IMAGE=$POOLER_IMAGE" >> $GITHUB_OUTPUT
+
       - name: Define UI image name
         id: image_ui
         run: |
@@ -69,6 +76,15 @@ jobs:
           tags: "${{ steps.image.outputs.OPERATOR_IMAGE }}"
           platforms: linux/amd64,linux/arm64
 
+      - name: Build and push multiarch pooler image to ghcr
+        uses: docker/build-push-action@v3
+        with:
+          context: pooler
+          push: true
+          build-args: BASE_IMAGE=alpine:3.19
+          tags: "${{ steps.image_pooler.outputs.POOLER_IMAGE }}"
+          platforms: linux/amd64,linux/arm64
+
       - name: Build and push multiarch ui image to ghcr
         uses: docker/build-push-action@v3
         with: