Cloud Firestore is a nosql database offering on Firebase. Cloud SQL Postgres is a database offering on GCP.
Firebase Cloud Functions (FCF) are 'serverless functions'. You upload some code that looks like an Express app. I personally use the npm package 'apollo-server-cloud-functions' to provide Apollo Server GraphQL endpoints using 'type-graphql'. If you do it right, there is very little vendor lockin. I theoretically could use this same code on Nhost.
Since it is all Google, Firebase can 'talk' to anything on GCP. Thus, my FCF can use 'mikro-orm' to talk to my cloud sql postgres database.
I know, a lot of names... but once you wrap your head around it all, it starts to get a bit easier. The nice thing about all of this is that I get one small usage based bill every month and it just magically runs without any devops or thought on my part.