chore: Add .repo-metadata.json file for java-core (#9250)

Fixes: #9249 

File is pulled from https://togithub.com/googleapis/java-core/blob/66212871e334db68a3f603aab919ede9d97c56b3/.repo-metadata.json
diff --git a/java-core/.repo-metadata.json b/java-core/.repo-metadata.json
new file mode 100644
index 0000000..e065a3e
--- /dev/null
+++ b/java-core/.repo-metadata.json
@@ -0,0 +1,10 @@
+{
+  "api_shortname": "google-cloud-core",
+  "name_pretty": "Google Cloud Core",
+  "release_level": "stable",
+  "language": "java",
+  "repo": "googleapis/google-cloud-java",
+  "repo_short": "java-core",
+  "library_type": "CORE",
+  "distribution_name": "com.google.cloud:google-cloud-core"
+}
\ No newline at end of file