BUG: Convert output type in Excel for MultiIndex with period levels

pandas/tests/io/excel/test_style.py

@@ -338,7 +338,8 @@ def test_styler_to_s3(s3_public_bucket, s3so):
         tm.assert_frame_equal(result, df)
 
 
-def test_format_hierarchical_rows_periodindex_merge_cells():
+@pytest.mark.parametrize("merge_cells", [True, False])
+def test_format_hierarchical_rows_periodindex(merge_cells):
     # GH#60099
     df = DataFrame(
         {"A": [1, 2]},
@@ -347,25 +348,7 @@ def test_format_hierarchical_rows_periodindex_merge_cells():
             names=["date", "category"],
         ),
     )
-    formatter = ExcelFormatter(df, merge_cells=True)
-    formatted_cells = list(formatter._format_hierarchical_rows())
-
-    for cell in formatted_cells:
-        assert not isinstance(
-            cell.val, Period
-        ), "Period should be converted to Timestamp"
-
-
-def test_format_hierarchical_rows_periodindex_no_merge_cells():
-    # GH#60099
-    df = DataFrame(
-        {"A": [1, 2]},
-        index=MultiIndex.from_arrays(
-            [period_range("2023-01", "2023-02", freq="M"), ["X", "Y"]],
-            names=["date", "category"],
-        ),
-    )
-    formatter = ExcelFormatter(df, merge_cells=False)
+    formatter = ExcelFormatter(df, merge_cells=merge_cells)
     formatted_cells = list(formatter._format_hierarchical_rows())
 
     for cell in formatted_cells:

pandas/tests/io/excel/test_writers.py

@@ -25,6 +25,7 @@
     MultiIndex,
     date_range,
     option_context,
+    period_range,
 )
 import pandas._testing as tm
 
@@ -1549,3 +1550,27 @@ def test_subclass_attr(klass):
     attrs_base = {name for name in dir(ExcelWriter) if not name.startswith("_")}
     attrs_klass = {name for name in dir(klass) if not name.startswith("_")}
     assert not attrs_base.symmetric_difference(attrs_klass)
+
+
+@pytest.mark.parametrize("merge_cells", [True, False])
+def test_excel_round_trip_with_periodindex(merge_cells, engine):
+    # GH#60099
+    df = DataFrame(
+        {"A": [1, 2]},
+        index=MultiIndex.from_arrays(
+            [period_range("2023-01", "2023-02", freq="M"), ["X", "Y"]],
+            names=["date", "category"],
+        ),
+    )
+
+    with BytesIO() as buffer:
+        with ExcelWriter(buffer) as writer:
+            df.to_excel(writer, merge_cells=merge_cells)
+
+        buffer.seek(0)
+        result_df = pd.read_excel(buffer, index_col=[0, 1])
+        result_df.index = result_df.index.set_levels(
+            [result_df.index.levels[0].to_period("M"), result_df.index.levels[1]]
+        )
+
+    tm.assert_frame_equal(df, result_df)