what are the external database which are supported by Zeebe ?
Zeebe doesn’t use a database. It uses a replicated append-only event log. Watch this video: https://www.youtube.com/watch?v=JbXKgQQmukE
But you could export to an external database/storage. You just need to write the exporter for that.
Out of the box it comes with an exporter for ElasticSearch (for use with Operate), and people have used it with Postgres and MySQL with the Zeebe Simple Monitor project.
I wrote an article about writing an exporter, and wrote an example exporter for the EventStore database: https://zeebe.io/blog/2019/05/exporter-part-2/