BUG: infer_freq throws exception on Series of timezone-aware Timestamps

[cai-lw]

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• 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

index = pd.date_range('2023-01-01', '2023-01-03', tz='America/Los_Angeles')
series = index.to_series().reset_index(drop=True)
object_series = series.astype(object)

for data in [index, series, object_series]:
    print('type:', type(data))
    print('dtype:', data.dtype)
    try:
        freq = pd.infer_freq(data)
        print('success, freq is', freq)
    except Exception as e:
        print(str(e))

Issue Description

When given a Series of timezone-aware Timestamps, infer_freq throws an exception. However, if given a DatetimeIndex of the exact same sequence of timezone-aware Timestamps, it works just fine. The problem comes from that DatetimeTZDtype is not allowed when checking the dtype of the Series. Adding is_datetime64tz_dtype to the dtype check should fix this issue.

pandas/pandas/tseries/frequencies.py

Lines 151 to 159 in 8daf188

	if not (
	is_datetime64_dtype(values)
	or is_timedelta64_dtype(values)
	or values.dtype == object
	):
	raise TypeError(
	"cannot infer freq from a non-convertible dtype "
	f"on a Series of {index.dtype}"
	)

Note that, although the documentation says the input type must be DatetimeIndex or TimedeltaIndex, the type annotation does include Series. The discrepancy among documentation, type annotation, and implementation (which accepts Series and converts it into DatetimeIndex when possible) should also be fixed.

pandas/pandas/tseries/frequencies.py

Lines 115 to 117 in 8daf188

	def infer_freq(
	index: DatetimeIndex | TimedeltaIndex | Series | DatetimeLikeArrayMixin,
	) -> str | None:

Actual output of the example:

type: <class 'pandas.core.indexes.datetimes.DatetimeIndex'>
dtype: datetime64[ns, America/Los_Angeles]
success, freq is D
type: <class 'pandas.core.series.Series'>
dtype: datetime64[ns, America/Los_Angeles]
cannot infer freq from a non-convertible dtype on a Series of datetime64[ns, America/Los_Angeles]
type: <class 'pandas.core.series.Series'>
dtype: object
success, freq is D

Expected Behavior

infer_freq should accept Series of timezone-aware timestamps, convert it into DateTimeIndex, and proceed as usual.

Installed Versions

INSTALLED VERSIONS
------------------
commit           : 478d340667831908b5b4bf09a2787a11a14560c9
python           : 3.9.6.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 22.4.0
Version          : Darwin Kernel Version 22.4.0: Mon Mar  6 20:59:28 PST 2023; root:xnu-8796.101.5~3/RELEASE_ARM64_T6000
machine          : arm64
processor        : arm
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 2.0.0
numpy            : 1.24.2
pytz             : 2022.2.1
dateutil         : 2.8.2
setuptools       : 58.0.4
pip              : 23.0
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : 4.9.1
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 3.1.2
IPython          : 8.5.0
pandas_datareader: None
bs4              : 4.11.1
bottleneck       : None
brotli           : None
fastparquet      : None
fsspec           : None
gcsfs            : None
matplotlib       : None
numba            : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pyreadstat       : None
pyxlsb           : None
s3fs             : None
scipy            : 1.10.0
snappy           : None
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
zstandard        : None
tzdata           : 2023.3
qtpy             : 2.2.0
pyqt5            : None