For what it’s worth, I don’t have sqlite3 installed but can use the sqlite3 module in the python3.10 venv of HA:
(homeassistant) homeassistant@hassbian:~/.homeassistant $ python3
Python 3.10.9 (main, Feb 2 2023, 09:53:17) [GCC 10.2.1 20210110] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import sqlite3
>>> print(sqlite3.version)
2.6.0
But it is an old version compared to the one you installed.
In your linked post, did you try the solution of exporting the LD_LIBRARY_PATH before starting hass as suggested in post #18