[SPARK-31321][SQL] Remove SaveMode check in v2 FileWriteBuilder

### What changes were proposed in this pull request?

The `SaveMode` is resolved before we create `FileWriteBuilder` to build `BatchWrite`.

In #25876, we removed save mode for DSV2 from DataFrameWriter. So that the `mode` method is never used which makes `validateInputs` fail determinately without `mode` set.

### Why are the changes needed?
rm dead code.

### Does this PR introduce any user-facing change?

no

### How was this patch tested?

existing tests.

Closes #28090 from yaooqinn/SPARK-31321.

Authored-by: Kent Yao <yaooqinn@hotmail.com>
Signed-off-by: Wenchen Fan <wenchen@databricks.com>
(cherry picked from commit 1ce584f)
Signed-off-by: Wenchen Fan <wenchen@databricks.com>

Author: yaooqinn

sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/v2/FileWriteBuilder.scala

@@ -16,7 +16,6 @@
  */
 package org.apache.spark.sql.execution.datasources.v2
 
-import java.io.IOException
 import java.util.UUID
 
 import scala.collection.JavaConverters._
@@ -27,7 +26,7 @@ import org.apache.hadoop.mapreduce.Job
 import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat
 
 import org.apache.spark.internal.io.FileCommitProtocol
-import org.apache.spark.sql.{AnalysisException, SaveMode, SparkSession}
+import org.apache.spark.sql.{AnalysisException, SparkSession}
 import org.apache.spark.sql.catalyst.InternalRow
 import org.apache.spark.sql.catalyst.util.{CaseInsensitiveMap, DateTimeUtils}
 import org.apache.spark.sql.connector.write.{BatchWrite, LogicalWriteInfo, WriteBuilder}
@@ -46,12 +45,6 @@ abstract class FileWriteBuilder(
   private val schema = info.schema()
   private val queryId = info.queryId()
   private val options = info.options()
-  private var mode: SaveMode = _
-
-  def mode(mode: SaveMode): WriteBuilder = {
-    this.mode = mode
-    this
-  }
 
   override def buildForBatch(): BatchWrite = {
     val sparkSession = SparkSession.active
@@ -68,26 +61,8 @@ abstract class FileWriteBuilder(
     lazy val description =
       createWriteJobDescription(sparkSession, hadoopConf, job, paths.head, options.asScala.toMap)
 
-    val fs = path.getFileSystem(hadoopConf)
-    mode match {
-      case SaveMode.ErrorIfExists if fs.exists(path) =>
-        val qualifiedOutputPath = path.makeQualified(fs.getUri, fs.getWorkingDirectory)
-        throw new AnalysisException(s"path $qualifiedOutputPath already exists.")
-
-      case SaveMode.Ignore if fs.exists(path) =>
-        null
-
-      case SaveMode.Overwrite =>
-        if (fs.exists(path) && !committer.deleteWithJob(fs, path, true)) {
-          throw new IOException(s"Unable to clear directory $path prior to writing to it")
-        }
-        committer.setupJob(job)
-        new FileBatchWrite(job, description, committer)
-
-      case _ =>
-        committer.setupJob(job)
-        new FileBatchWrite(job, description, committer)
-    }
+    committer.setupJob(job)
+    new FileBatchWrite(job, description, committer)
   }
 
   /**
@@ -104,7 +79,6 @@ abstract class FileWriteBuilder(
   private def validateInputs(caseSensitiveAnalysis: Boolean): Unit = {
     assert(schema != null, "Missing input data schema")
     assert(queryId != null, "Missing query ID")
-    assert(mode != null, "Missing save mode")
 
     if (paths.length != 1) {
       throw new IllegalArgumentException("Expected exactly one path to be specified, but " +