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Reproducible Example

>>> import pandas as pd
>>> pd.Series().dtype
dtype('O')  # ok
>>> pd.Series(index=[]).dtype
dtype('float64')  # not ok

Issue Description

Corner case of #49342, where the dtype of an empty Series become float64, where it should be object.

Expected Behavior

Empty Series should always be of type object.

Installed Versions

INSTALLED VERSIONS ------------------ commit : bb7dd2c85dff62b7cce2262f6ba6c3ecb1013153 python : 3.9.7.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 : 2.0.0.dev0+606.gbb7dd2c85d.dirty numpy : 1.23.3 pytz : 2022.1 dateutil : 2.8.2 setuptools : 65.5.0 pip : 22.2.2 Cython : 0.29.32 pytest : 7.1.2 hypothesis : 6.37.0 sphinx : 5.0.2 blosc : 1.10.6 feather : None xlsxwriter : None lxml.etree : 4.9.1 html5lib : None pymysql : 1.0.2 psycopg2 : 2.9.3 jinja2 : 3.1.2 IPython : 7.29.0 pandas_datareader: None bs4 : 4.11.1 bottleneck : None brotli : fastparquet : 0.8.3 fsspec : 2022.10.0 gcsfs : None matplotlib : 3.5.2 numba : 0.56.4 numexpr : 2.8.3 odfpy : None openpyxl : None pandas_gbq : None pyarrow : 10.0.0 pyreadstat : None pyxlsb : None s3fs : 2022.10.0 scipy : 1.9.1 snappy : None sqlalchemy : None tables : 3.7.0 tabulate : 0.9.0 xarray : None xlrd : None zstandard : 0.18.0 tzdata : None qtpy : None pyqt5 : None