My ultimate goal is to differentiate/manage the cost on databricks (azure) based on different teams/project.
And I was thinking whether I could utilize workspace to achieve this.
I read below , it sounds like workspace can access a cluster, but does not say whether multiple workspace can access the same cluster or not.
A Databricks workspace is an environment for accessing all of your Databricks assets. The workspace organizes objects (notebooks, libraries, and experiments) into folders, and provides access to data and computational resources such as clusters and jobs.
In other words, can I creat a cluster and somehow ensure can be only accessed by certain project or team or workspace?
To manage whom can access a particular cluster, you can make use of cluster access control. With cluster access control, you can determine what users can do on the cluster. E.g. attach to the cluster, the ability to restart it or to fully manage it. You can do this on a user level but also on a user group level. Note that you have to be on Azure Databricks Premium Plan to make use of cluster access control.
You also mentioned that your ultimate goal is to differentiate/manage costs on Azure Databricks. For this you can make use of tags. You can tag workspaces, clusters and pools which are then propagated to cost analysis reports in the Azure portal (see here).