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BUG: Indexing with pd.Float(32|64)Dtype indexes is different than with numpy float indexes #51053

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@topper-123

Description

@topper-123

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Reproducible Example

>>> import pandas as pd
>>>
>>> np_idx = pd.Index([1, 0, 1], dtype="float64")  # numpy dtype
>>> pd.Series(range(3), index=np_idx)[1]  # ok
1.0    0
1.0    2
dtype: int64
>>> pd_idx = pd.Index([1, 0, 1], dtype="Float64") # pandas dtype
>>> pd.Series(range(3), index=pd_idx)[1]  # not ok
1

Likewise with setting using indexing:

>>> ser = pd.Series(range(3), index=np_idx)
>>> ser[1] = 10
>>> ser  # ok
1.0    10
0.0     1
1.0    10
dtype: int64
>>> ser = pd.Series(range(3), index=pd_idx)
>>> ser[1] = 10
>>> ser  # not ok
1.0     0
0.0    10
1.0     2
dtype: int64

Issue Description

Indexing using Series.__getitem__ & Series.__setitem__ (likewise for DataFrame) using integers on float indexes behaves differently, depending on if the the dtype is an extension float dtype or not.

The reason is that NumericIndex._should_fallback_to_positional is always False, while Index._should_fallback_to_positional is only False is the index is inferred to be integer-like (infer_dtype returns "integer" or "mixed-integer").

The better solution would be for Index._should_fallback_to_positional to be Falseif its dtype is a real dtype (int, uint or float numpy or ExtensionDtype).

Expected Behavior

Indexing using a pandas float dtype should behave the same as for a numpy float dtype (except nan-related behaviour).

Installed Versions

INSTALLED VERSIONS

commit : 8dab54d
python : 3.8.11.final.0
python-bits : 64
OS : Darwin
OS-release : 21.6.0
Version : Darwin Kernel Version 21.6.0: Wed Aug 10 14:28:35 PDT 2022; root:xnu-8020.141.5~2/RELEASE_ARM64_T8101
machine : arm64
processor : arm
byteorder : little
LC_ALL : None
LANG : None
LOCALE : None.UTF-8

pandas : 1.5.2
numpy : 1.23.4
pytz : 2022.1
dateutil : 2.8.2
setuptools : 65.5.0
pip : 22.2.2
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : 8.7.0
pandas_datareader: None
bs4 : None
bottleneck : 1.3.5
brotli :
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : 2.8.4
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
snappy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
zstandard : None
tzdata : None

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