The third estate takes care of the universal affairs of society. These are above all the civil servants.

What does it live on?

It must be free from labor for its own needs. Either it has enough resources of its own. Or the state pays it. So it finds its own advantage precisely in its work for the universal.

Summary: The universal estate works for the common good. To make this possible, it has resources of its own, or the state secures its livelihood. So in this estate, private interest and the universal coincide.