chore: address PR comments.

Author: arpan14

google-cloud-spanner/src/main/java/com/google/cloud/spanner/Spanner.java

@@ -30,8 +30,7 @@ public interface Spanner extends Service<SpannerOptions>, AutoCloseable {
   /**
    * Returns a {@code DatabaseAdminClient} to execute admin operations on Cloud Spanner databases.
    *
-   * @return
-   * @deprecated Use {@link #databaseAdminClient()} instead.
+   * @return {@code DatabaseAdminClient}
    */
   /*
    * <!--SNIPPET get_dbadmin_client-->
@@ -42,7 +41,6 @@ public interface Spanner extends Service<SpannerOptions>, AutoCloseable {
    * }</pre>
    * <!--SNIPPET get_dbadmin_client-->
    */
-  @Deprecated
   DatabaseAdminClient getDatabaseAdminClient();
 
   /**
@@ -68,7 +66,6 @@ default com.google.cloud.spanner.admin.database.v1.DatabaseAdminClient databaseA
    * Returns an {@code InstanceAdminClient} to execute admin operations on Cloud Spanner instances.
    *
    * @return {@code InstanceAdminClient}
-   * @deprecated Use {@link #instanceAdminClient()}} instead.
    */
   /*
    * <!--SNIPPET get_instance_admin_client-->
@@ -79,7 +76,6 @@ default com.google.cloud.spanner.admin.database.v1.DatabaseAdminClient databaseA
    * }</pre>
    * <!--SNIPPET get_instance_admin_client-->
    */
-  @Deprecated
   InstanceAdminClient getInstanceAdminClient();
 
   /**

google-cloud-spanner/src/main/java/com/google/cloud/spanner/SpannerImpl.java

@@ -101,6 +101,16 @@ private static String nextDatabaseClientId(DatabaseId databaseId) {
   @GuardedBy("this")
   private final Map<DatabaseId, DatabaseClientImpl> dbClients = new HashMap<>();
 
+  @GuardedBy("this")
+  private final Map<
+          InstanceAdminStub, com.google.cloud.spanner.admin.instance.v1.InstanceAdminClient>
+      instanceAdminClients = new HashMap<>();
+
+  @GuardedBy("this")
+  private final Map<
+          DatabaseAdminStub, com.google.cloud.spanner.admin.database.v1.DatabaseAdminClient>
+      databaseAdminClients = new HashMap<>();
+
   private final CloseableExecutorProvider asyncExecutorProvider;
 
   @GuardedBy("this")
@@ -109,6 +119,9 @@ private static String nextDatabaseClientId(DatabaseId databaseId) {
   private final DatabaseAdminClient dbAdminClient;
   private final InstanceAdminClient instanceClient;
 
+  private final com.google.cloud.spanner.admin.database.v1.DatabaseAdminClient databaseAdminClient;
+  private final com.google.cloud.spanner.admin.instance.v1.InstanceAdminClient instanceAdminClient;
+
   /**
    * Exception class used to track the stack trace at the point when a Spanner instance is closed.
    * This exception will be thrown if a user tries to use any resources that were returned by this
@@ -137,6 +150,12 @@ static final class ClosedException extends RuntimeException {
     this.dbAdminClient = new DatabaseAdminClientImpl(options.getProjectId(), gapicRpc);
     this.instanceClient =
         new InstanceAdminClientImpl(options.getProjectId(), gapicRpc, dbAdminClient);
+    this.databaseAdminClient =
+        com.google.cloud.spanner.admin.database.v1.DatabaseAdminClient.create(
+            gapicRpc.getDatabaseAdminStub());
+    this.instanceAdminClient =
+        com.google.cloud.spanner.admin.instance.v1.InstanceAdminClient.create(
+            gapicRpc.getInstanceAdminStub());
   }
 
   SpannerImpl(SpannerOptions options) {
@@ -211,8 +230,7 @@ public DatabaseAdminClient getDatabaseAdminClient() {
 
   @Override
   public com.google.cloud.spanner.admin.database.v1.DatabaseAdminClient databaseAdminClient() {
-    DatabaseAdminStub databaseAdminStub = gapicRpc.getDatabaseAdminStub();
-    return com.google.cloud.spanner.admin.database.v1.DatabaseAdminClient.create(databaseAdminStub);
+    return databaseAdminClient;
   }
 
   @Override
@@ -222,8 +240,7 @@ public InstanceAdminClient getInstanceAdminClient() {
 
   @Override
   public com.google.cloud.spanner.admin.instance.v1.InstanceAdminClient instanceAdminClient() {
-    InstanceAdminStub instanceAdminStub = gapicRpc.getInstanceAdminStub();
-    return com.google.cloud.spanner.admin.instance.v1.InstanceAdminClient.create(instanceAdminStub);
+    return instanceAdminClient;
   }
 
   @Override