BUG: [pyarrow] TypeError: '<' not supported between instances of 'datetime.datetime' and 'str'

[randolf-scholz]

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 numpy as np
import pandas as pd

t = pd.date_range("2023-01-01", "2023-01-04", freq="1h")
x = np.random.randn(len(t))
df = pd.DataFrame(x, index=t, columns=["values"])

df.to_parquet("frame.parquet")
df2 = pd.read_parquet("frame.parquet", dtype_backend="pyarrow")

df["2023-01-01":"2023-01-02"]  # ✔
df2["2023-01-01":"2023-01-02"]  # ✘ TypeError: '<' not supported between instances of 'datetime.datetime' and 'str'

Issue Description

Slicing a DataFrame with index type timestamp[us][pyarrow] does not work with strings.

Expected Behavior

The operation should do the same thing regardless of the dtype backend.

Installed Versions

INSTALLED VERSIONS
------------------
commit           : 965ceca9fd796940050d6fc817707bba1c4f9bff
python           : 3.11.3.final.0
python-bits      : 64
OS               : Linux
OS-release       : 5.19.0-43-generic
Version          : #44~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Mon May 22 13:39:36 UTC 2
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 2.0.2
numpy            : 1.23.5
pytz             : 2023.3
dateutil         : 2.8.2
setuptools       : 67.7.2
pip              : 23.1.2
Cython           : 0.29.34
pytest           : 7.3.1
hypothesis       : None
sphinx           : 7.0.0
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : 4.9.2
html5lib         : None
pymysql          : 1.0.3
psycopg2         : None
jinja2           : 3.1.2
IPython          : 8.13.2
pandas_datareader: None
bs4              : 4.12.2
bottleneck       : None
brotli           : None
fastparquet      : 2023.4.0
fsspec           : 2023.5.0
gcsfs            : None
matplotlib       : 3.7.1
numba            : 0.57.0
numexpr          : 2.8.4
odfpy            : None
openpyxl         : 3.1.2
pandas_gbq       : None
pyarrow          : 12.0.0
pyreadstat       : None
pyxlsb           : None
s3fs             : None
scipy            : 1.10.1
snappy           : None
sqlalchemy       : 1.4.48
tables           : 3.8.0
tabulate         : 0.9.0
xarray           : 2023.4.2
xlrd             : None
zstandard        : None
tzdata           : 2023.3
qtpy             : None
pyqt5            : None

[mroeschke]

Thanks for the report. This is essentially a duplicate of #53154 so closing