Hi Gabrielle,
The browse permission is getting it from the user account for the VSA. A commcell role wont effect this.
Here is the documentation for vSphere user accounts
https://documentation.commvault.com/commvault/v11_sp20/article?p=32132.htm
And then you can customise the user for limited scope
You can restrict a user account to a specific entity as described in Adding a Custom User with Limited Scope; but the user must also have permissions for all parent objects of the entity. For example, if you define a user account with permissions on an ESX server, you must also give that user permissions on the vCenter and datacenter. If you select the option to propagate permissions to all child objects, the user can back up all virtual machines on the ESX server.