Just searching for SQLite replication will get you several options to research to fit your requirements. The concept of multi active and no size limit you would simply solve with a sharding mechanism that you layer on top through a data access method.

But if you're looking for some monolith project to provide all of this for you you're going to be in that territory of that fake open source. Because again to build all of this into one tool that has everything from the data access layer all the way down to the metal underneath to ensure that it's replicated and highly available is not a trivial task. Especially if you want things like acid compliance arbitrary joins between data structures and so forth.

The file system is effectively a database of things with an API that accesses those things. Simply a file system of properly named files and directories could meet your needs depending on what those are.

It's the complexity of your access model and methods that will determine what fits your bill.