Yeah, there are SQLite forks or products built on SQLite which have these sorts of features, but SQLite doesn't. They remains reasons why someone may want to use another database (such as PostgreSQL, or an SQLite fork, or a database which uses SQLite as a storage engine) instead of SQLite.
Honestly though, if I need these sorts of distribution features, I would probably prefer the database to have them built in. I don't really see the point in using SQLite at that scale.
They're probably not as battle tested as the PostgreSQL ones, but they are around, have users, and are actively developed.
The ones I remember off the top of my head:
* https://litestream.io
* https://github.com/rqlite/rqlite <-- more of a "distributed database using RAFT" type of thing
* https://github.com/canonical/dqlite