gcloud sql export does not allow to export multiple databases from the same instance (It seems it was supported in the past but could not achieve it now).
Offloading the exports to another instance (serverless export) takes too much time. I wonder if the same instance can be used to avoid the initialization time. Essentially running sequentially export operations for a specific instance that will reach out to the same pre-provisioned serverless instance.
For now it is not possible and a new instance will be created per database.