BUG: DateTimeIndex asof() broken by mixed frequency / non-midnight times

[hagrid67]

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
dr1 = pd.date_range("2021-08-05", "2021-08-10", freq="1D")
print(dr1)  # prints dates only
print(dr1.asof("2021-08-09"))  # correctly prints 2021-08-09 00:00:00
# dr2 = dr1.append(pd.DatetimeIndex(["2021-08-11 00:00:00"]))  # adding a midnight time works fine
dr2 = dr1.append(pd.DatetimeIndex(["2021-08-11 00:00:01"]))   # non-midnight time breaks asof
print(dr2)  # prints dates and times, now that there is a non-midnight time - this is fine.
# wrongly prints 2021-08-06 00:00:00 even though 2021-08-09 exists in Index:
print("This should be 2021-08-09: ", dr2.asof("2021-08-09"))  
print("2021-08-09" in dr2)  # True, so why does asof not find it?

Issue Description

Using a daily DateTimeIndex, if an entry is appended which does not have a midnight time, then asof() can no longer find existing midnight datetimes.
I have reproduced the problem with 1.5.2, 1.5.3 and the nightly build '2.0.0.dev0+1147.g7cb7592523' (see below), all with Python 3.10.

Expected Behavior

dr2.asof("2021-08-09") should return "2021-08-09"

Installed Versions

INSTALLED VERSIONS

commit : 7cb7592
python : 3.10.4.final.0
python-bits : 64
OS : Linux
OS-release : 5.13.0-35-generic
Version : #40~20.04.1-Ubuntu SMP Mon Mar 7 09:18:32 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+1147.g7cb7592523
numpy : 1.23.5
pytz : 2022.1
dateutil : 2.8.2
setuptools : 44.0.0
pip : 22.3.1
Cython : None
pytest : 7.2.0
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : 3.0.6
lxml.etree : 4.9.1
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.7.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : None
brotli : 1.0.9
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : 3.6.1
numba : None
numexpr : None
odfpy : None
openpyxl : 3.0.10
pandas_gbq : None
pyarrow : 10.0.0
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.9.3
snappy : None
sqlalchemy : 0.7.10
tables : None
tabulate : 0.9.0
xarray : None
xlrd : 2.0.1
zstandard : None
tzdata : None
qtpy : 2.1.0
pyqt5 : None

[hagrid67]

I reproduced the problem with the nightly build - is that the same as the "main branch"? (as per the link above)

[hagrid67]

Seems I can get around it using one of the following:

dr2.asof(pd.to_datetime("2021-08-09"))
dr2.asof("2021-08-09 00:00:00")