[CI] [GHA] Use an internal image for docker buildx setup (openvinot…

…oolkit#27380)

Should eliminate the problem of getting images from public Docker Hub:
https://github.com/openvinotoolkit/openvino/actions/runs/11652494488/job/32456237021?pr=27374

Ticket: 156671

.github/actions/handle_docker/action.yml

@@ -46,6 +46,9 @@ runs:
     - name: Set up Docker Buildx
       id: buildx
       uses: docker/setup-buildx-action@v3
+      with:
+        driver-opts: |
+          image=${{ inputs.registry }}/dockerio/moby/buildkit:buildx-stable-1
 
     - name: Handle docker images
       id: handle_images
@@ -62,7 +65,7 @@ runs:
         --base_tag_file "base/${{ inputs.dockerfiles_root_dir }}/docker_tag" \
         --docker_env_changed "${{ fromJSON(inputs.changed_components).docker_env }}" \
         --dockerfiles_changed "${{ fromJSON(inputs.changed_components).dockerfiles }}" \
-        --docker_builder "${{ steps.buildx.outputs.name}}" \
+        --docker_builder "${{ steps.buildx.outputs.name }}" \
         --repo "${{ github.repository }}" \
         --ref_name "${{ github.ref_name }}" \
         $([[ -n $pr ]] && echo "--pr $pr" || echo '-s ${{ github.sha }}') \

.github/dockerfiles/docker_tag

@@ -1 +1 @@
-pr-26993
+pr-27380