[SPARK-50378][SS] Add custom metric for tracking spent for proc initi…

…al state in transformWithState

### What changes were proposed in this pull request?
Add custom metric for tracking spent for proc initial state in transformWithState

### Why are the changes needed?
Adds tracking for time spent in populating initial state

### Does this PR introduce _any_ user-facing change?
No

### How was this patch tested?
Added unit tests

```
[info] Run completed in 2 minutes, 38 seconds.
[info] Total number of tests run: 22
[info] Suites: completed 1, aborted 0
[info] Tests: succeeded 22, failed 0, canceled 0, ignored 0, pending 0
[info] All tests passed.
```

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

Closes #48913 from anishshri-db/task/SPARK-50378.

Authored-by: Anish Shrigondekar <anish.shrigondekar@databricks.com>
Signed-off-by: Jungtaek Lim <kabhwan.opensource@gmail.com>

sql/core/src/main/scala/org/apache/spark/sql/execution/streaming/TransformWithStateExec.scala

@@ -410,6 +410,9 @@ case class TransformWithStateExec(
   // operator specific metrics
   override def customStatefulOperatorMetrics: Seq[StatefulOperatorCustomMetric] = {
     Seq(
+      // metrics around initial state
+      StatefulOperatorCustomSumMetric("initialStateProcessingTimeMs",
+        "Number of milliseconds taken to process all initial state"),
       // metrics around state variables
       StatefulOperatorCustomSumMetric("numValueStateVars", "Number of value state variables"),
       StatefulOperatorCustomSumMetric("numListStateVars", "Number of list state variables"),
@@ -655,6 +658,8 @@ case class TransformWithStateExec(
     statefulProcessor.init(outputMode, timeMode)
     processorHandle.setHandleState(StatefulProcessorHandleState.INITIALIZED)
 
+    val initialStateProcTimeMs = longMetric("initialStateProcessingTimeMs")
+    val initialStateStartTimeNs = System.nanoTime
     // Check if is first batch
     // Only process initial states for first batch
     if (processorHandle.getQueryInfo().getBatchId == 0) {
@@ -667,6 +672,7 @@ case class TransformWithStateExec(
           processInitialStateRows(keyRow.asInstanceOf[UnsafeRow], valueRowIter)
       }
     }
+    initialStateProcTimeMs += NANOSECONDS.toMillis(System.nanoTime - initialStateStartTimeNs)
 
     processDataWithPartition(childDataIterator, store, processorHandle)
   }

sql/core/src/test/scala/org/apache/spark/sql/streaming/TransformWithStateInitialStateSuite.scala

@@ -395,6 +395,10 @@ class TransformWithStateInitialStateSuite extends StateStoreMetricsTest
         AddData(inputData, InitInputRow("k2", "update", 40.0)),
         AddData(inputData, InitInputRow("non-exist", "getOption", -1.0)),
         CheckNewAnswer(("non-exist", "getOption", -1.0)),
+        Execute { q =>
+          assert(q.lastProgress
+            .stateOperators(0).customMetrics.get("initialStateProcessingTimeMs") > 0)
+        },
         AddData(inputData, InitInputRow("k1", "appendList", 37.0)),
         AddData(inputData, InitInputRow("k2", "appendList", 40.0)),
         AddData(inputData, InitInputRow("non-exist", "getList", -1.0)),
@@ -514,6 +518,10 @@ class TransformWithStateInitialStateSuite extends StateStoreMetricsTest
         AdvanceManualClock(1 * 1000),
         // registered timer for "a" and "b" is 6000, first batch is processed at ts = 1000
         CheckNewAnswer(("c", "1")),
+        Execute { q =>
+          assert(q.lastProgress
+            .stateOperators(0).customMetrics.get("initialStateProcessingTimeMs") > 0)
+        },
 
         AddData(inputData, "c"),
         AdvanceManualClock(6 * 1000), // ts = 7000, "a" expires