1st Party Publishers
In an ideal world, publishers would not exist and writers would be compensated fairly and immediately. In a slightly less ideal world, music publishing companies would not need multiple entities. But, in this world, many do.
There are multiple performance rights organizations in the US, and they have this rule that if a writer is affiliated with one of them (and can be affiliated with only one), then all publishers in the chain must be affiliated with the same PRO.
As consequence, all but the smallest US publishers have multiple entities.
Some CMOs world-wide have a rule that a publisher can only be affiliated with them, and not with any other CMO anywhere. (This is happening less and less, but it is still happening.)
So, if a publisher wants to register directly with them, they need a separate entity.
Some publishers have other reasons for having multiple entities, including (bad) software they use.
That Green Thing deals with this in a very simple way. You mark your entities as first-party publishers. In some aspects, That Green Thing will treat them as one entity, and in others as multiple.
Just as you do.