Unifying the world doesn't mean unifying Europe to the Urals.It means Rome has to take over all of Afro-Eurasia from the Atlantic to the Cape to the Pacific to the Indonesian archipelago. It then has to take over the ANZA region, and then has to conquer both Americas. That is what unifying the world requires. And even Eurofed can't see that happening, which is to his credit.
But you were talking about pre-modern conquests in Persia and India and I didn't mention any of that. By the time this Rome is taking large chunks of sub-Saharian Africa and Asia it's already in a very modern age.
But even so they are not conquering it all. Other states get more and more dependent of Rome and fall into its sphere one way or the other. Some could even apply to become a province in order to receive parliamentary representation, a route similar to OTL Sikkim within the Republic of India.
The soft power of TTL *contemporary Rome would make OTL USA a joke.