BUG: grouped.last() will sometimes turn a boolean column into Int64

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 pandas as pd

df = pd.DataFrame(
    {
        'id': [1, 2, 3, 4],
        'test': [True, pd.NA, pd.NA, False]
    }
).convert_dtypes()

grouped = df.groupby('id')
bad = grouped.last()
assert bad.test.dtype == pd.BooleanDtype() # fails

Issue Description

On the latest master this returns an Int64 column.

    test
id
1      1
2   <NA>
3   <NA>
4      0

I checked 1.4.0 and it properly returns the boolean dtype.

     test
id
1    True
2    <NA>
3    <NA>
4   False

What is weird is that changing 3. to True/False will give the proper dtype.

Expected Behavior

Retain the boolean dtype from df.test.

Installed Versions

INSTALLED VERSIONS

commit : 663147edd35bc3e0362f7d637c8d5f5e597f961b python : 3.10.0.final.0 python-bits : 64 OS : Linux OS-release : 5.16.12-arch1-1 Version : #1 SMP PREEMPT Wed, 02 Mar 2022 12:22:51 +0000 machine : x86_64 processor : byteorder : little LC_ALL : None LANG : en_US.UTF-8 LOCALE : en_US.UTF-8

pandas : 1.5.0.dev0+545.g663147edd3 numpy : 1.21.5 pytz : 2021.3 dateutil : 2.8.2 pip : 21.3.1 setuptools : 58.5.3 Cython : 0.29.28 pytest : 6.2.5 hypothesis : None sphinx : None blosc : None feather : None xlsxwriter : None lxml.etree : 4.7.1 html5lib : None pymysql : None psycopg2 : None jinja2 : 3.0.3 IPython : 7.29.0 pandas_datareader: None bs4 : 4.10.0 bottleneck : None brotli : None fastparquet : None fsspec : None gcsfs : None markupsafe : 2.0.1 matplotlib : None numba : 0.55.1 numexpr : None odfpy : None openpyxl : 3.0.9 pandas_gbq : None pyarrow : 8.0.0.dev230+gb2ae3d74d pyreadstat : None pyxlsb : None s3fs : None scipy : 1.8.0 snappy : None sqlalchemy : 2.0.0b1 tables : None tabulate : 0.8.9 xarray : None xlrd : None xlwt : None zstandard : None

[ayeshaam]

take

[sydneyeh]

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