How do I know the usage of storage on managed database?

MySQL/MariaDB keep information like this within the database itself in the *_schema tables. These are queryable by users with the proper credentials. These tables are well-documented.

You will probably have to do some math on the raw query results to get what you want.

Here's an example relative to (what I perceive was) your specific request:

https://stackoverflow.com/questions/1733507/how-to-get-size-of-mysql-database

You'll have to the notification part yourself…

-- sw

I understand that I need to monitor the usage myself for now.
Thank you.