List of tasks that can be done by only dbadmin user

In regards to the MC, information about roles and privileges can be found in Vertica's documentation: https://my.vertica.com/docs/9.0.x/HTML/index.htm#Authoring/ManagementConsole/GettingStartedWithMC/MCUsersRolesPrivileges.htm

Anything done by admintools (dbadmin linux user) is definitely admin only.
You can get a list of all internal functions that are dbadmin only with:
select procedure_name from where is_superuser;
You can get the list of all superuser tables with:
select table_name from system_tables where is_superuser_only order by table_name;