feat: install compatibility check (googleapis#1508)

* feat: install clirr check

* install an independent action

* format changes

* change name

* change action name

.github/workflows/ci-maven.yaml

@@ -151,6 +151,21 @@ jobs:
         # Exclude the root project
         run: mvn -B -ntp fmt:check
 
+  compatibility:
+    runs-on: ubuntu-22.04
+    steps:
+      - uses: actions/checkout@v3
+      - uses: actions/setup-java@v3
+        with:
+          java-version: 11
+          distribution: temurin
+          cache: maven
+      - run: java -version
+      - name: Compatibility check
+        #  package jar so that gapic-generator-java module can use
+        #  testlib modules of gax
+        run: mvn package clirr:check -DskipTests
+
   showcase:
     runs-on: ubuntu-22.04
     strategy: