ci: Use Java 8 for Linkage Checker (#3716)

Manual invocation:
https://github.com/googleapis/sdk-platform-java/actions/runs/14038997003

Author: lqiu96

.github/workflows/downstream_protobuf_compatibility_check_nightly.yaml

@@ -47,7 +47,13 @@ jobs:
         uses: actions/checkout@v4
       - uses: actions/setup-java@v4
         with:
-          # Use Java 11 for this as Linkage Checker is only compatible with Java 11 or below
+          java-version: 8
+          distribution: temurin
+      - run: echo "JAVA8_HOME=${JAVA_HOME}" >> $GITHUB_ENV
+      # Java Client Libraries are compiled with Java 11 and target Java 8. Java 11 is required because GraalVM
+      # minimum support is for Java 11.
+      - uses: actions/setup-java@v4
+        with:
           java-version: 11
           distribution: temurin
       - name: Print Protobuf-Java testing version

.kokoro/nightly/downstream-protobuf-binary-compatibility.sh

@@ -62,6 +62,7 @@ function build_program_arguments() {
   done
 }
 
+# TODO(https://github.com/GoogleCloudPlatform/cloud-opensource-java/issues/2395): Java 17+ support for Linkage Checker
 # cloud-opensource-java contains the Linkage Checker tool
 git clone https://github.com/GoogleCloudPlatform/cloud-opensource-java.git
 pushd cloud-opensource-java

.kokoro/nightly/downstream-protobuf-source-compatibility.sh

@@ -28,11 +28,17 @@ for repo in ${REPOS_UNDER_TEST//,/ }; do # Split on comma
   git clone "https://github.com/googleapis/$repo.git" --depth=1
   pushd "$repo"
 
+  # Compile with Java 11 and run the tests with Java 8
+  mvn clean compile -T 1C
+
+  export JAVA_HOME="${JAVA8_HOME}"
+  export PATH=$JAVA_HOME/bin:$PATH
+
   # Compile the Handwritten Library with the Protobuf-Java version to test source compatibility
   # Run unit tests to help check for any behavior differences (dependant on coverage)
   if [ "${repo}" == "google-cloud-java" ]; then
     # The `-am` command also builds anything these libraries depend on (i.e. proto-* and grpc-* sub modules)
-    mvn clean test -B -V -ntp \
+    mvn test -B -V -ntp \
       -Dclirr.skip \
       -Denforcer.skip \
       -Dmaven.javadoc.skip \
@@ -41,7 +47,7 @@ for repo in ${REPOS_UNDER_TEST//,/ }; do # Split on comma
       -pl "${google_cloud_java_handwritten_maven_args}" -am \
       -T 1C
   else
-    mvn clean test -B -V -ntp \
+    mvn test -B -V -ntp \
       -Dclirr.skip \
       -Denforcer.skip \
       -Dmaven.javadoc.skip \