Unlike what many people think, the use of "emperor of the Greeks" by the Latins did not completely replace the title "emperor of the Romans"; both could be used and actually were used together
After reading some parts of the Council of Florence, I found the ways the papal Latins referred to the Eastern emperor interesting and even a bit intriguing
In the first mention, in session 3, John is clearly called emperor of the Greeks: "Those on whom the power of choosing the place devolved, passed a decree which was accepted by the ambassadors of our most dear son in Christ John, emperor of the Greeks, and of our venerable brother Joseph, patriarch of Constantinople."
But by session 4, the Latins already use a friendlier title: "Finally, our most dear son John Palacologus, emperor of the Romans, together with our venerable brother Joseph." Session 6 even adds a little more: "Eugenius, bishop, servant of the servants of God, for an everlasting record. With the agreement of our most dear son John Palaeologus, illustrious emperor of the Romans."
It gets even more curious in session 19: "Also that the emperor of the Greeks and their church shall have due honour, that is to say, what it had when the present schism began, always saving the rights, honours, privileges and dignities of the supreme pontiff and the Roman church and the emperor of the Romans." Not only are both titles used for the emperor, but they appear in the exact same sentence!
The title the Latins used was not exactly the same as the one they gave to the German emperor. In Eugenius IV’s letter to John VIII, he addresses the emperor as "Paleologo Romeorum imperatore" which is slightly different from the classical title that used "romanorum". Even so, this difference seems to exist only in Latin, since the official Italian translation of the letter made by the Vatican simplifies the title to "Imperatore dei Romani", which is the same title used for figures like Barbarossa or Charlemagne
Sources:
The Council of Florence: https://www.ewtn.com/catholicism/library/ecumenical-council-of-florence-1438-1445-1461
Bulla Laetentur Caeli to John VIII Palaiologos: https://www.vatican.va/content/eugenius-iv/la/documents/bulla-laetentur-caeli-6-iulii-1439.html