[SPARK-54174][CORE][CONNECT][TESTS] Remove override of deprecated method SparkThrowable#getErrorClass in Spark code

### What changes were proposed in this pull request?
This pr removes the override of the deprecated method `SparkThrowable#getErrorClass` from the Spark codebase. Since this method has been marked as deprecated and is defined as `default String getErrorClass() { return getCondition(); }`, the overriding behavior for it can be omitted based on the current code.

### Why are the changes needed?
Code Cleanup

### Does this PR introduce _any_ user-facing change?
No, this only involves test code.

### How was this patch tested?
Pass Github Actions

### Was this patch authored or co-authored using generative AI tooling?
No

Closes #52868 from LuciferYang/cleanup-override-getErrorClass.

Lead-authored-by: yangjie01 <yangjie01@baidu.com>
Co-authored-by: YangJie <yangjie01@baidu.com>
Signed-off-by: Dongjoon Hyun <dongjoon@apache.org>

Author: LuciferYang

core/src/test/scala/org/apache/spark/SparkThrowableSuite.scala

@@ -620,7 +620,6 @@ class SparkThrowableSuite extends SparkFunSuite {
     // Create a custom throwable that overrides getDefaultMessageTemplate.
     class CustomTemplatedThrowable extends Throwable with SparkThrowable {
       override def getCondition: String = "DIVIDE_BY_ZERO"
-      override def getErrorClass: String = "DIVIDE_BY_ZERO"
       override def getMessage: String = "Custom message"
       override def getMessageParameters: java.util.Map[String, String] =
         Map("config" -> "TEST_CONFIG").asJava
@@ -643,7 +642,6 @@ class SparkThrowableSuite extends SparkFunSuite {
     // Create a throwable that uses default getDefaultMessageTemplate implementation.
     class ReadFromJSONThrowable extends Throwable with SparkThrowable {
       override def getCondition: String = "DIVIDE_BY_ZERO"
-      override def getErrorClass: String = "DIVIDE_BY_ZERO"
       override def getMessage: String = "Random message"
       override def getMessageParameters: java.util.Map[String, String] =
         Map("config" -> "TEST_CONFIG").asJava
@@ -665,7 +663,6 @@ class SparkThrowableSuite extends SparkFunSuite {
     // Create a throwable with non-existing error condition.
     class NonExistingConditionThrowable extends Throwable with SparkThrowable {
       override def getCondition: String = "NON_EXISTING_ERROR_CONDITION"
-      override def getErrorClass: String = "NON_EXISTING_ERROR_CONDITION"
       override def getMessage: String = "Non-existing error message"
       override def getMessageParameters: java.util.Map[String, String] =
         Map("param" -> "value").asJava

sql/connect/server/src/test/scala/org/apache/spark/sql/connect/service/FetchErrorDetailsHandlerSuite.scala

@@ -46,7 +46,6 @@ class TestSparkThrowableWithBreakingChange(
     with SparkThrowable {
 
   override def getCondition: String = errorClass
-  override def getErrorClass: String = errorClass
   override def getMessageParameters: java.util.Map[String, String] = {
     import scala.jdk.CollectionConverters._
     messageParams.asJava