I believe that streaming changes from SQLite is what https://sqlsync.dev/ is
It uses a custom VFS, memory journal mode, and bypasses SQLite for optimistic concurrency handling. I dunno how it handles crash safety, or if it even uses the same on disk file format.
My point here is not that this is impossible, it's that SQlite's WAL implementation isn't meant to be pluggable, and Litestream is a very clever hack, that requires a very specific setup to work well.
It takes a fair amount of work to replicate that in other environments.