Is it also foreseen for test projects to conduct transfer and capacity-building activities themselves or will this be facilitated and implemented only by the project type that facilitates results amplification, e.g., governance projects?

Test projects can initiate a transfer/capacity building activity following the pilot actions, although it should not be their main focus, as we also have a Transfer project type. However, if your intention is to apply for a Transfer project on the basis of your Test project, it could be a good idea to start preparing the ground for wider transfer.
The governance projects will support transfer and capacity-building at Mission level building synergies, but it is not their role to transfer directly your results.