In a Databricks customer's cloud account, the primary elements stored include:

Data: This is the central type of content stored in the customer's cloud account. Data might include various datasets, tables, and files that are used and managed through Databricks platforms.

Notebooks: These are also stored within a customer's cloud account. Notebooks include scripts, notes, and other information necessary for data analysis and processing tasks.

Cluster management metadata is indeed managed through the cloud, but it's primarily handled by Databricks rather than stored directly in the customer's account. The Databricks web application itself is not stored within the customer's cloud account; rather, it's a service provided by Databricks.