sqlite3_rsync exists:

https://sqlite.org/rsync.html

... and is installed and available:

  # sqlite3_rsync -vv ./test.db [email protected]:test.db

"Ordinary rsync does not understand SQLite transactions. Rsync will make a copy of ORIGIN into REPLICA, however the copy might not be consistent. Parts of the copy might be from one transaction, while other parts might be from a different transaction. The database copy might be corrupt."