since 1805 C4C offers the possibility to transport UI Changes, Page Layout, Business Roles, Language Adaptation etc.
However, I was not able to find a possibility within the selectable "UI Change"-Options to transport the "Home"-Page and it's tile-customization for different business roles.
Is this possible or do I have to do it for both systems - test and production?
You will have to do this manually in each tenant. Please consider voting or raising as a new idea on the Customer Influence tool. Typically homepages are impacted by reports being migrated to each tenant so we should see some traction here if analytics are included in the transport management functionality in the future.