found a first working solution

Author: SaturnFromTitan

doc/source/whatsnew/v1.1.0.rst

@@ -56,6 +56,7 @@ Other API changes
 - :meth:`Series.describe` will now show distribution percentiles for ``datetime`` dtypes, statistics ``first`` and ``last``
   will now be ``min`` and ``max`` to match with numeric dtypes in :meth:`DataFrame.describe` (:issue:`30164`)
 - :meth:`Groupby.groups` now returns an abbreviated representation when called on large dataframes (:issue:`1135`)
+- :class:`Series` constructor will default to construct an :class:`Index`, rather than an :class:`RangeIndex` when constructed with empty data, matching the behaviour of ``data=None``.
 
 Backwards incompatible API changes
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

pandas/core/series.py

@@ -299,7 +299,12 @@ def __init__(
             if index is None:
                 if not is_list_like(data):
                     data = [data]
-                index = ibase.default_index(len(data))
+
+                if is_empty_data(data):
+                    index = Index([])
+                else:
+                    index = ibase.default_index(len(data))
+
             elif is_list_like(data):
 
                 # a scalar numpy array is list-like but doesn't

pandas/tests/extension/base/missing.py

@@ -20,7 +20,7 @@ def test_isna(self, data_missing):
         # GH 21189
         result = pd.Series(data_missing).drop([0, 1]).isna()
         expected = pd.Series([], dtype=bool)
-        self.assert_series_equal(result, expected)
+        self.assert_series_equal(result, expected, check_index_type=False)
 
     def test_dropna_array(self, data_missing):
         result = data_missing.dropna()

pandas/tests/extension/decimal/test_decimal.py

@@ -86,7 +86,7 @@ def convert(x):
         else:
             right_na = right.isna()
 
-        tm.assert_series_equal(left_na, right_na)
+        tm.assert_series_equal(left_na, right_na, *args, **kwargs)
         return tm.assert_series_equal(left[~left_na], right[~right_na], *args, **kwargs)
 
     @classmethod

pandas/tests/extension/test_sparse.py

@@ -186,7 +186,7 @@ def test_isna(self, data_missing):
         # GH 21189
         result = pd.Series(data_missing).drop([0, 1]).isna()
         expected = pd.Series([], dtype=expected_dtype)
-        self.assert_series_equal(result, expected)
+        self.assert_series_equal(result, expected, check_index_type=False)
 
     def test_fillna_limit_pad(self, data_missing):
         with tm.assert_produces_warning(PerformanceWarning):

pandas/tests/groupby/test_grouping.py

@@ -641,7 +641,7 @@ def test_groupby_empty(self):
         gr = s.groupby([])
 
         result = gr.mean()
-        tm.assert_series_equal(result, s)
+        tm.assert_series_equal(result, s, check_index_type=False)
 
         # check group properties
         assert len(gr.grouper.groupings) == 1

pandas/tests/io/json/test_pandas.py

@@ -678,7 +678,7 @@ def test_series_roundtrip_empty(self, orient, numpy):
         else:
             expected.index = expected.index.astype(float)
 
-        tm.assert_series_equal(result, expected)
+        tm.assert_series_equal(result, expected, check_index_type=False)
 
     @pytest.mark.parametrize("numpy", [True, False])
     def test_series_roundtrip_timeseries(self, orient, numpy):

pandas/tests/reductions/test_reductions.py

@@ -1090,7 +1090,7 @@ class TestSeriesMode:
     def test_mode_empty(self, dropna, expected):
         s = Series([], dtype=np.float64)
         result = s.mode(dropna)
-        tm.assert_series_equal(result, expected)
+        tm.assert_series_equal(result, expected, check_index_type=False)
 
     @pytest.mark.parametrize(
         "dropna, data, expected",

pandas/tests/reshape/test_concat.py

@@ -736,17 +736,28 @@ def test_concat_categorical_empty(self):
         s1 = pd.Series([], dtype="category")
         s2 = pd.Series([], dtype="category")
 
-        tm.assert_series_equal(pd.concat([s1, s2], ignore_index=True), s2)
-        tm.assert_series_equal(s1.append(s2, ignore_index=True), s2)
+        tm.assert_series_equal(
+            pd.concat([s1, s2], ignore_index=True), s2, check_index_type=False
+        )
+        tm.assert_series_equal(
+            s1.append(s2, ignore_index=True), s2, check_index_type=False
+        )
 
         s1 = pd.Series([], dtype="category")
         s2 = pd.Series([], dtype="object")
 
         # different dtype => not-category
-        tm.assert_series_equal(pd.concat([s1, s2], ignore_index=True), s2)
-        tm.assert_series_equal(s1.append(s2, ignore_index=True), s2)
-        tm.assert_series_equal(pd.concat([s2, s1], ignore_index=True), s2)
-        tm.assert_series_equal(s2.append(s1, ignore_index=True), s2)
+        result = pd.concat([s1, s2], ignore_index=True)
+        tm.assert_series_equal(result, s2, check_index_type=False)
+
+        result = s1.append(s2, ignore_index=True)
+        tm.assert_series_equal(result, s2, check_index_type=False)
+
+        result = pd.concat([s1, s2], ignore_index=True)
+        tm.assert_series_equal(result, s2, check_index_type=False)
+
+        result = s2.append(s1, ignore_index=True)
+        tm.assert_series_equal(result, s2, check_index_type=False)
 
         s1 = pd.Series([], dtype="category")
         s2 = pd.Series([np.nan, np.nan])
@@ -2202,7 +2213,7 @@ def test_concat_empty_series_timelike(self, tz, values):
             }
         )
         result = concat([first, second], axis=1)
-        tm.assert_frame_equal(result, expected)
+        tm.assert_frame_equal(result, expected, check_index_type=False)
 
     def test_default_index(self):
         # is_series and ignore_index

pandas/tests/series/test_api.py

@@ -497,7 +497,7 @@ async def test_tab_complete_warning(self, ip):
         pytest.importorskip("IPython", minversion="6.0.0")
         from IPython.core.completer import provisionalcompleter
 
-        code = "import pandas as pd; s = pd.Series()"
+        code = "import pandas as pd; s = pd.Series(dtype=object)"
         await ip.run_code(code)
         with tm.assert_produces_warning(None):
             with provisionalcompleter("ignore"):