You're right! To the Romans, every Roman citizen was a Roman. There was no "genetically Roman" category. The OP's "genetic" category is indeed a "made up concept", as you say! And the reason they made it up is the reason I stated above.

>It’s like how peasants used to say that the King is a divine representative of God, because that was the king and the system’s con job back then, to make the dumb peasants obedient through religion.

Well no one really knows because most of this comes from the writing ruling classes. If we're talking Middle Ages and the Modern Age, France offers an interesting example : absolute monarchy by divine right came very late (17th cent) and was almost never fully accepted. The system relied greatly on religion (which kept one's standing within a social class), weak origin stories (the Franks came and conquered the Gallo-Romans/ my ancestor fought in the crusades, which is why you're a serf), and a very strong system of local rights and privileges (I'm a legitimate ruler because I keep your right to hold poultry markets on Sundays, which the next village doesn't have).

The divine dimension you refer to was a constant effort in France and England (where the king was not a religious ruler) well described in "The Royal Touch" by Marc Bloch.