[CI] Update the requirements for the push_image workflows

.github/workflows/push_image.yml

@@ -11,6 +11,15 @@ jobs:
     - name: clang-format
       run: |
         docker run --rm -v ${PWD}:/src  wiiuenv/clang-format:13.0.0-2 -r ./include ./libraries
+  build-lib:
+    runs-on: ubuntu-18.04
+    needs: clang-format-lib
+    steps:
+    - uses: actions/checkout@v2
+    - name: build binary
+      run: |
+        docker build . -f Dockerfile.buildlocal -t builder
+        docker run --rm -v ${PWD}:/project builder make
   clang-format-examples:
     runs-on: ubuntu-18.04
     steps:
@@ -30,7 +39,7 @@ jobs:
         docker run --rm -v ${PWD}:/project builder make
   push_image:
     runs-on: ubuntu-latest
-    needs: clang-format-lib
+    needs: [build-lib, build-examples]
     steps:
     - uses: actions/checkout@master
     - name: Get release version