workflows: release use make for docs checks

Since the Makefile has a target for generating and checking that there's
no diff between what's been generated and what's versioned, we don't
need custom logic to perform the check, so we reuse this target for that
step.

.github/workflows/notify-integration-release-via-manual.yaml

@@ -22,17 +22,9 @@ jobs:
           ref: ${{ github.event.inputs.branch }}
       # Ensure that Docs are Compiled
       - uses: actions/setup-go@93397bea11091df50f3d7e59dc26a7711a8bcfbe # v4.1.0
-      - shell: bash
-        run: make generate
-      - shell: bash
-        run: |
-          if [[ -z "$(git status -s)" ]]; then
-            echo "OK"
-          else
-            echo "Docs have been updated, but the compiled docs have not been committed."
-            echo "Run 'make generate', and commit the result to resolve this error."
-            exit 1
-          fi
+      - name: check docs are up-to-date
+        shell: bash
+        run: make check-generate
       # Perform the Release
       - name: Checkout integration-release-action
         uses: actions/checkout@8e5e7e5ab8b370d6c329ec480221332ada57f0ab # v3.5.2