BUG: TimedeltaIndex and Index[timedelta] behave differently upon __rtruediv__ #62712
Description
Pandas version checks
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I have checked that this issue has not already been reported.
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I have confirmed this bug exists on the latest version of pandas.
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I have confirmed this bug exists on the main branch of pandas.
Reproducible Example
from datetime import timedelta
from typing import reveal_type
import pandas as pd
timedeltaindex = pd.Index([pd.Timedelta(seconds=1)]) * [1]
reveal_type(timedeltaindex) # TimedeltaIndex, contains pd.Timedelta
reveal_type(timedelta(seconds=1) / timedeltaindex) # Index, no error
index_timedelta = pd.Index([1]) * [pd.Timedelta(seconds=1)]
reveal_type(index_timedelta) # Index, contains datetime.timedelta
reveal_type(timedelta(seconds=1) / index_timedelta) # errorIssue Description
In #62524 I've shown that Index[timedelta] instead of TimedeltaIndex can be produced.
Here I found that these objects behave differently when rtruedived by another timedelta.
Expected Behavior
Consistently giving Index[float]
Installed Versions
INSTALLED VERSIONS
commit : 4665c10
python : 3.12.10
python-bits : 64
OS : Windows
OS-release : 11
Version : 10.0.26100
machine : AMD64
processor : AMD64 Family 25 Model 116 Stepping 1, AuthenticAMD
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : Czech_Czechia.1252
pandas : 2.3.2
numpy : 2.3.4
pytz : 2025.2
dateutil : 2.9.0.post0
pip : 24.2
Cython : None
sphinx : None
IPython : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.14.2
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
html5lib : 1.1
hypothesis : None
gcsfs : None
jinja2 : 3.1.6
lxml.etree : 6.0.2
matplotlib : 3.10.6
numba : None
numexpr : 2.13.1
odfpy : None
openpyxl : 3.1.5
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 21.0.0
pyreadstat : 1.3.1
pytest : 8.4.2
python-calamine : None
pyxlsb : 1.0.10
s3fs : None
scipy : 1.16.2
sqlalchemy : 2.0.43
tables : 3.10.2
tabulate : 0.9.0
xarray : 2025.9.1
xlrd : 2.0.2
xlsxwriter : 3.2.9
zstandard : None
tzdata : 2025.2
qtpy : None
pyqt5 : None