The Databricks web application is the user interface that allows you to create and manage workspaces, clusters, notebooks, jobs, and other resources. It is hosted completely in the control plane of the classic Databricks architecture, which includes the backend services that Databricks manages in your Databricks account. The other options are part of the compute plane, which is where your data is processed by compute resources such as clusters. The compute plane is in your own cloud account and network.
References: Databricks architecture overview, Security and Trust Center