CI: Add job for pip check (#64058)

.github/workflows/ci.yaml

@@ -36,6 +36,7 @@ jobs:
       tests_glob: ${{ steps.info.outputs.tests_glob }}
       test_groups: ${{ steps.info.outputs.test_groups }}
       test_group_count: ${{ steps.info.outputs.test_group_count }}
+      requirements: ${{ steps.core.outputs.requirements }}
     runs-on: ubuntu-latest
     steps:
       - name: Check out code from GitHub
@@ -671,6 +672,38 @@ jobs:
           python --version
           mypy homeassistant/components/${{ needs.changes.outputs.integrations_glob }}
 
+  pip-check:
+    runs-on: ubuntu-latest
+    if: needs.changes.outputs.requirements == 'true'
+    needs:
+      - changes
+      - prepare-tests
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: [3.9]
+    name: Run pip check ${{ matrix.python-version }}
+    container: homeassistant/ci-azure:${{ matrix.python-version }}
+    steps:
+      - name: Check out code from GitHub
+        uses: actions/checkout@v2.4.0
+      - name: Restore full Python ${{ matrix.python-version }} virtual environment
+        id: cache-venv
+        uses: actions/cache@v2.1.7
+        with:
+          path: venv
+          key: ${{ runner.os }}-${{ matrix.python-version }}-${{
+            needs.prepare-tests.outputs.python-key }}
+      - name: Fail job if Python cache restore failed
+        if: steps.cache-venv.outputs.cache-hit != 'true'
+        run: |
+          echo "Failed to restore Python virtual environment from cache"
+          exit 1
+      - name: Run pip check
+        run: |
+          . venv/bin/activate
+          ./script/pip_check $PIP_CACHE
+
   pytest:
     runs-on: ubuntu-latest
     if: needs.changes.outputs.test_full_suite == 'true' || needs.changes.outputs.tests_glob