I assume he wants a proper database and to be honest if you have zero interaction between the things you are partitioning on it's very easy to scale with SQLite or any other database.
There's no reason you can't either run more servers or multiple instances of postgres per server, with docker or otherwise.
I'm probably going to try using Citus Data instead of moving to Cassandra if I ever get big. We'll see.
I honestly don't see why you wouldn't consider SQLite to be a "proper database." I think it has a reasonably competitive feature set.
In a usecase where you consider independent databases, with few interactions between them, for millions of users (and a few MBs + binary blobs of data per user) I'd certainly consider it as a possible solution.
There's no reason you can't either run more servers or multiple instances of postgres per server, with docker or otherwise.
I'm probably going to try using Citus Data instead of moving to Cassandra if I ever get big. We'll see.