BUG: Cannot `shift` Intervals that are not `closed='right'` (the default)

[WillMorrisonEnspi]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd
pd.Series([pd.Interval(1, 2, closed='left'), pd.Interval(2, 3, closed='left')]).shift(1)

Issue Description

This line in shift creates an empty IntervalArray without specifying which side the intervals are closed on. When that array and the one being shifted get concatenated, the following exception is raised:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/wmorrison/.local/share/pyenv/versions/3.11.5/envs/3.11.5-enspired@aws_lambda/lib/python3.11/site-packages/pandas/core/generic.py", line 11228, in shift
    new_data = self._mgr.shift(periods=periods, fill_value=fill_value)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/wmorrison/.local/share/pyenv/versions/3.11.5/envs/3.11.5-enspired@aws_lambda/lib/python3.11/site-packages/pandas/core/internals/base.py", line 312, in shift
    return self.apply_with_block("shift", periods=periods, fill_value=fill_value)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/wmorrison/.local/share/pyenv/versions/3.11.5/envs/3.11.5-enspired@aws_lambda/lib/python3.11/site-packages/pandas/core/internals/managers.py", line 363, in apply
    applied = getattr(b, f)(**kwargs)
              ^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/wmorrison/.local/share/pyenv/versions/3.11.5/envs/3.11.5-enspired@aws_lambda/lib/python3.11/site-packages/pandas/core/internals/blocks.py", line 2020, in shift
    new_values = self.values.T.shift(periods=periods, fill_value=fill_value).T
                 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/wmorrison/.local/share/pyenv/versions/3.11.5/envs/3.11.5-enspired@aws_lambda/lib/python3.11/site-packages/pandas/core/arrays/interval.py", line 1097, in shift
    return self._concat_same_type([a, b])
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/wmorrison/.local/share/pyenv/versions/3.11.5/envs/3.11.5-enspired@aws_lambda/lib/python3.11/site-packages/pandas/core/arrays/interval.py", line 1045, in _concat_same_type
    raise ValueError("Intervals must all be closed on the same side.")
ValueError: Intervals must all be closed on the same side.

Expected Behavior

The following pd.Series[Interval] should be returned, closed on the same side as the original Series

0           NaN
1    [1.0, 2.0)
dtype: interval

Installed Versions

INSTALLED VERSIONS

commit : 0691c5c
python : 3.11.5
python-bits : 64
OS : Linux
OS-release : 6.8.0-48-generic
Version : #48~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Mon Oct 7 11:24:13 UTC 2
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.3
numpy : 2.1.3
pytz : 2024.2
dateutil : 2.9.0.post0
pip : 24.3.1
Cython : None
sphinx : None
IPython : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.3
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
html5lib : None
hypothesis : None
gcsfs : None
jinja2 : 3.1.4
lxml.etree : None
matplotlib : 3.9.2
numba : None
numexpr : None
odfpy : None
openpyxl : 3.1.5
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : None
pyreadstat : None
pytest : 8.3.3
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.14.1
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlsxwriter : None
zstandard : None
tzdata : 2024.2
qtpy : None
pyqt5 : None

[rhshadrach]

Thanks for the report! Further investigations and PRs to fix are welcome.

[veronicabenedict]

take