the Precursor Confederacy, was the name of the Precursor based government that ruled or rather controlled the Multiverse during their reign. Much of the information about it comes from Archaios Fylakas, the Confederacy is still largely unknown to us, how their society functioned, how their government works and all, but the information given to us is still useful, especially sense before hand, the Multiverse had virtually no information about the Precursors at all.
although the exact history of the Precursors is still a mystery to us, but from what Archaios have stated, the Precursors were a peaceful carnivorous species that prefer peace over all, unifying their homeworld peacefully. But once they reached the stars, the Precursors had to deal with conflicts with other species every once and a while. She also have told that the Precursors had the habit of uplifting species throughout their history, even if it only lead to conflicts, the Precursors continued to do these upliftings. Eventually the Precursors unified their universe under their banner and created a Confederacy, a Confederacy that lasted until the Precursors, as well as most species in the Multiverse at that time, extinction.
the Precursor's Confederacy is loose based Federation of sorts between numerous species and their empires and the Precursors and it's empire, but was largely controlled by the Precursors. However, independent empires also fall into this if they were allied with the Precursors, overall, the information given to use about the Confederacy is, more or less, a mixed between a Federation of sorts and a complexed systems of alliance between various empires and the Precursors. the Confederacy itself was headed by a Protector, the highest position one can get in the Confederacy and is not just for the Precursors to hold, however, most of the Protectors were Precursors, though as to what the Protectors were, is yet to be determined.