ci: linkage monitor CI job to use build.sh (#375)

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Synth log will be available here:
https://source.cloud.google.com/results/invocations/549c8707-14a7-4963-9d20-bbd5d5285b08/targets

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Source-Link: googleapis/synthtool@f327d3b

java-core/.github/workflows/ci.yaml

@@ -55,17 +55,10 @@ jobs:
         java-version: 8
     - run: java -version
     - name: Install artifacts to local Maven repository
-      run: |
-        source .kokoro/common.sh
-        retry_with_backoff 3 10 \
-            mvn install -B -V \
-                -Dmaven.test.skip -DskipTests=true \
-                -Dclirr.skip=true \
-                -Denforcer.skip=true \
-                -Dmaven.javadoc.skip=true \
-                -Dgcloud.download.skip=true
+      run: .kokoro/build.sh
       shell: bash
-    - uses: GoogleCloudPlatform/cloud-opensource-java/linkage-monitor@v1-linkagemonitor
+    - name: Validate any conflicts with regard to com.google.cloud:libraries-bom (latest release)
+      uses: GoogleCloudPlatform/cloud-opensource-java/linkage-monitor@v1-linkagemonitor
   lint:
     runs-on: ubuntu-latest
     steps:

java-core/synth.metadata

@@ -4,14 +4,14 @@
       "git": {
         "name": ".",
         "remote": "https://github.com/googleapis/java-core.git",
-        "sha": "313193509ee7fa0e694188f9266c54c029a582c6"
+        "sha": "dc4473fe6321e825c38140d729249cce7e40cc8b"
       }
     },
     {
       "git": {
         "name": "synthtool",
         "remote": "https://github.com/googleapis/synthtool.git",
-        "sha": "2414b817065726eae0bc525346c7e874f969369d"
+        "sha": "f327d3b657a63ae4a8efd7f011a15eacae36b59c"
       }
     }
   ],