BUG: empty strings raise in non-ISO8601 formats but parse as NaT elsewhere

[MarcoGorelli]

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

In [1]: to_datetime(['2020-01-01', ''], format='%Y-%m-%d')  # works
Out[1]: DatetimeIndex(['2020-01-01', 'NaT'], dtype='datetime64[ns]', freq=None)

In [2]: to_datetime(['2020-01-01', ''], format='%Y-%d-%m')  # fails
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[2], line 1
----> 1 to_datetime(['2020-01-01', ''], format='%Y-%d-%m')

File ~/pandas-dev/pandas/core/tools/datetimes.py:1098, in to_datetime(arg, errors, dayfirst, yearfirst, utc, format, exact, unit, infer_datetime_format, origin, cache)
   1096         result = _convert_and_box_cache(argc, cache_array)
   1097     else:
-> 1098         result = convert_listlike(argc, format)
   1099 else:
   1100     result = convert_listlike(np.array([arg]), format)[0]

File ~/pandas-dev/pandas/core/tools/datetimes.py:442, in _convert_listlike_datetimes(arg, format, name, utc, unit, errors, dayfirst, yearfirst, exact)
    439 require_iso8601 = format is not None and format_is_iso(format)
    441 if format is not None and not require_iso8601:
--> 442     return _to_datetime_with_format(
    443         arg,
    444         orig_arg,
    445         name,
    446         utc,
    447         format,
    448         exact,
    449         errors,
    450     )
    452 result, tz_parsed = objects_to_datetime64ns(
    453     arg,
    454     dayfirst=dayfirst,
   (...)
    461     exact=exact,
    462 )
    464 if tz_parsed is not None:
    465     # We can take a shortcut since the datetime64 numpy array
    466     # is in UTC

File ~/pandas-dev/pandas/core/tools/datetimes.py:543, in _to_datetime_with_format(arg, orig_arg, name, utc, fmt, exact, errors)
    540         return _box_as_indexlike(result, utc=utc, name=name)
    542 # fallback
--> 543 res = _array_strptime_with_fallback(arg, name, utc, fmt, exact, errors)
    544 return res

File ~/pandas-dev/pandas/core/tools/datetimes.py:485, in _array_strptime_with_fallback(arg, name, utc, fmt, exact, errors)
    481 """
    482 Call array_strptime, with fallback behavior depending on 'errors'.
    483 """
    484 try:
--> 485     result, timezones = array_strptime(
    486         arg, fmt, exact=exact, errors=errors, utc=utc
    487     )
    488 except OutOfBoundsDatetime:
    489     if errors == "raise":

File ~/pandas-dev/pandas/_libs/tslibs/strptime.pyx:198, in pandas._libs.tslibs.strptime.array_strptime()
    196         iresult[i] = NPY_NAT
    197         continue
--> 198     raise ValueError(f"time data '{val}' does not match "
    199                      f"format '{fmt}' (match)")
    200 if len(val) != found.end():

ValueError: time data '' does not match format '%Y-%d-%m' (match)

Issue Description

In both cases, the empty string should become NaT

Expected Behavior

In both cases, the empty string should become NaT

Installed Versions

INSTALLED VERSIONS

commit : 20411cb
python : 3.8.15.final.0
python-bits : 64
OS : Linux
OS-release : 5.10.102.1-microsoft-standard-WSL2
Version : #1 SMP Wed Mar 2 00:30:59 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_GB.UTF-8
LOCALE : en_GB.UTF-8

pandas : 2.0.0.dev0+919.g20411cb047
numpy : 1.23.5
pytz : 2022.6
dateutil : 2.8.2
setuptools : 65.5.1
pip : 22.3.1
Cython : 0.29.32
pytest : 7.2.0
hypothesis : 6.61.0
sphinx : 4.5.0
blosc : None
feather : None
xlsxwriter : 3.0.3
lxml.etree : 4.9.1
html5lib : 1.1
pymysql : 1.0.2
psycopg2 : 2.9.3
jinja2 : 3.1.2
IPython : 8.7.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : 1.3.5
brotli :
fastparquet : 2022.12.0
fsspec : 2021.11.0
gcsfs : 2021.11.0
matplotlib : 3.6.2
numba : 0.56.4
numexpr : 2.8.3
odfpy : None
openpyxl : 3.0.10
pandas_gbq : None
pyarrow : 9.0.0
pyreadstat : 1.2.0
pyxlsb : 1.0.10
s3fs : 2021.11.0
scipy : 1.9.3
snappy :
sqlalchemy : 1.4.45
tables : 3.7.0
tabulate : 0.9.0
xarray : 2022.12.0
xlrd : 2.0.1
zstandard : 0.19.0
tzdata : None
qtpy : None
pyqt5 : None
None