BUG: Regression how datetime64[ns] is saved in sqlite table

[maximiliank]

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
import datetime as dt
import sqlite3

df=pd.DataFrame({'t':[dt.datetime.now()]}, dtype='datetime64[ns]')
conn=sqlite3.connect('test.sqlite3')
df.to_sql('test', conn, if_exists='replace', index=False)
conn.close()

Issue Description

With pandas version 2.1.0 the content of the sqlite3 table is:

SELECT * FROM test;
1693426580

So it stores datetime64[ns] as epoch.

With pandas version < 2.1.0 the content would be a string:
2023-08-30 22:16:24.753962

Expected Behavior

Save the datetime64[ns] as string like in the previous pandas versions

Installed Versions

INSTALLED VERSIONS

commit : ba1cccd
python : 3.11.4.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 : C.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.1.0
numpy : 1.25.2
pytz : 2023.3
dateutil : 2.8.2
setuptools : 66.1.1
pip : 23.0.1
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader : None
bs4 : None
bottleneck : None
dataframe-api-compat: 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 : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None

[phofl]

#53743 cc @lithomas1