BUG: DatetimeIndex and Timestamp behave inconsistently with respect to pd.DateOffset

[guyguyguy1234]

• 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 master branch of pandas.

Reproducible Example

pd.DatetimeIndex([pd.to_datetime('2020-10-25').tz_localize('Europe/Berlin')]) + pd.DateOffset(hours=3) 
returns 
2020-10-25 03:00:00+01:00

while

pd.to_datetime('2020-10-25').tz_localize('Europe/Berlin') + pd.DateOffset(hours=3) 
returns 
Timestamp('2020-10-25 02:00:00+0100', tz='Europe/Berlin')

Issue Description

Mismatch between the outputs.

Here is the stackoverflow post describing in detail the issue.

Expected Behavior

Returning same datetime

Installed Versions

INSTALLED VERSIONS

commit : 73c6825
python : 3.9.4.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19041
machine : AMD64
processor : Intel64 Family 6 Model 165 Stepping 2, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United States.1252

pandas : 1.3.3
numpy : 1.19.5
pytz : 2021.1
dateutil : 2.8.1
pip : 21.2.4
setuptools : 52.0.0.post20210125
Cython : 0.29.23
pytest : 6.2.3
hypothesis : None
sphinx : 4.0.1
blosc : None
feather : None
xlsxwriter : 1.3.8
lxml.etree : 4.6.3
html5lib : 1.1
pymysql : None
psycopg2 : None
jinja2 : 2.11.3
IPython : 7.22.0
pandas_datareader: None
bs4 : 4.9.3
bottleneck : 1.3.2
fsspec : 0.9.0
fastparquet : None
gcsfs : None
matplotlib : 3.3.4
numexpr : 2.7.3
odfpy : None
openpyxl : 3.0.7
pandas_gbq : None
pyarrow : None
pyxlsb : 1.0.8
s3fs : None
scipy : 1.6.2
sqlalchemy : 1.4.7
tables : None
tabulate : None
xarray : None
xlrd : 2.0.1
xlwt : 1.3.0
numba : 0.53.1

[srotondo]

take

[srotondo]

That last commit was a typo from an unrelated PR, ignore that.