It can be deployed as a single docker container on your own infrastructure (which can still be serverless with things like Fargate).
Would something like this be interesting/useful to you?
I am trying to see if there are potential users that have started with firebase but have hit limitation (technical or pricing) and need a way to migrate without rewriting the entire UI (or maybe they like the sdk and want to keep it even if the UI rewrite is not painful)
They claim to be a replacement for Firebase with pgsql as a store