[SPARK-48045][PYTHON] Pandas API groupby with multi-agg-relabel ignores as_index=False

### What changes were proposed in this pull request?
In a Scenario where we use GroupBy in PySpark API with relabeling of aggregate columns and using as_index = False,
the columns with which we group by are not returned in the DataFrame. The change proposes to fix this bug.

Example:
ps.DataFrame({"a": [0, 0], "b": [0, 1]}).groupby("a", as_index=False).agg(b_max=("b", "max"))

Result:
_  b_max
0      1

Required Result:
_  a  b_max
0  0      1

### Why are the changes needed?
The relabeling part of the code only uses only the aggregate columns. In a scenario where as_index=True, it is not an issue as the columns with which we group by are included in the index. When as_index=False, we need to append the columns with which we grouped by to the relabeling code.

Please, check the commits/PR for the code changes

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

### How was this patch tested?
- Passed GA
- Passed Build tests
- Unit Tested including scenarios in addition to the one provided in the Jira ticket

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

Closes #46391 from sinaiamonkar-sai/SPARK-48045-2.

Authored-by: sai <saidatt@Saidatts-MBP.attlocal.net>
Signed-off-by: Hyukjin Kwon <gurwls223@apache.org>
diff --git a/python/pyspark/pandas/groupby.py b/python/pyspark/pandas/groupby.py
index ec47ab7..55627a4 100644
--- a/python/pyspark/pandas/groupby.py
+++ b/python/pyspark/pandas/groupby.py
@@ -308,6 +308,7 @@
             )
 
         if not self._as_index:
+            index_cols = psdf._internal.column_labels
             should_drop_index = set(
                 i for i, gkey in enumerate(self._groupkeys) if gkey._psdf is not self._psdf
             )
@@ -322,8 +323,12 @@
                 psdf = psdf.reset_index(level=should_drop_index, drop=drop)
             if len(should_drop_index) < len(self._groupkeys):
                 psdf = psdf.reset_index()
+            index_cols = [c for c in psdf._internal.column_labels if c not in index_cols]
+            if relabeling:
+                psdf = psdf[pd.Index(index_cols + list(order))]
+                psdf.columns = pd.Index([c[0] for c in index_cols] + list(columns))
 
-        if relabeling:
+        if relabeling and self._as_index:
             psdf = psdf[order]
             psdf.columns = columns  # type: ignore[assignment]
         return psdf
diff --git a/python/pyspark/pandas/tests/groupby/test_groupby.py b/python/pyspark/pandas/tests/groupby/test_groupby.py
index 5867f7b..b58bfdd 100644
--- a/python/pyspark/pandas/tests/groupby/test_groupby.py
+++ b/python/pyspark/pandas/tests/groupby/test_groupby.py
@@ -451,6 +451,27 @@
             pdf.groupby([("x", "a"), ("x", "b")]).diff().sort_index(),
         )
 
+    def test_aggregate_relabel_index_false(self):
+        pdf = pd.DataFrame(
+            {
+                "A": [0, 0, 1, 1, 1],
+                "B": ["a", "a", "b", "a", "b"],
+                "C": [10, 15, 10, 20, 30],
+            }
+        )
+        psdf = ps.from_pandas(pdf)
+
+        self.assert_eq(
+            pdf.groupby(["B", "A"], as_index=False)
+            .agg(C_MAX=("C", "max"))
+            .sort_values(["B", "A"])
+            .reset_index(drop=True),
+            psdf.groupby(["B", "A"], as_index=False)
+            .agg(C_MAX=("C", "max"))
+            .sort_values(["B", "A"])
+            .reset_index(drop=True),
+        )
+
 
 class GroupByTests(
     GroupByTestsMixin,