So from my understanding, theology at the time was focused on there only ever being one universal empire and one emperor that was the guardian of the church.
That's why Charlemagne was made Emperor of the Romans over the Byzantine Irene. That's why there was the constant fight between Frederick Barbarossa and the Byzantine emperor during the 3rd crusade.
And there's all the struggles over powers between the HRE and the Papacy.
So now I'm wondering if when the Church proclaimed the Spanish Habsburgs the "Catholic Monarchs" if it was an attempt to replace the HRE and the Austrian Habsburgs in the concept of the 'universal empire' without getting into all the legalities and precedents already set.
Like how during the Cuban missile crisis the US proclaimed a "quarantine" instead of a blockade because there's legal requirements necessary for a blockade. Same thing, different name.
No, Alexander VI had other reasons for the title. First and foremost, the title is Catholic in the very sense of pertaining to the Catholic church rather than "universal sovereign".
The concession of the title happens at two different moments: 1494 and 1496. In 1493, as evidenced by the diplomatic correspondence between Desprats (the Monarch's factotum in Rome) and the pope, an agreement had been reached so the monarchs would be granted the title of "Most Catholic" (molt catòlichs, in the Catalan original letter), but the proposal got eventually put in a drawer. Why? This was a classic do ut des, where the pope would reward Ferdinand and Isabella with a fancy title with protocolary prerogatives after Alexander VI's firstborn son got married to Ferdinand's cousin and received the title of Duke of Gandia. Alexander, of course, decided to wait to grant the title and use it as a reward. In late 1494, he was very dependent on Spanish assistance, knowing full well that the king of France was preparing an invasion of the Italian peninsula in order to get the crown of Naples. When the French invasion came in 1495 and the Spanish military assistance came in late and in insufficient numbers, the grant of the title of "Most Catholic Monarchs" was put in the fridge. That title would have come as some sort of way of slapping the king of France in the face, as he was the "Most Christian King", and both Alexander and Desprats knew that, but with F&I's lack of serious intervention in defence of the pope, they would not be "worthy" of the grand title that Desprats and Alexander had been working on.
When the Spanish help finally arrived for good, the pontificial position in Italy was consolidated. The French capitulated in Atella in 1496, and their defeat was complete, something that could not have happened without the help of Ferdinand and Isabella. Alexander's heart warmed up a bit, so he resucitated the proposal of the title of Most Catholic Monarchs, but he switched the denomination to Catholic Monarchs instead. This had not been the first idea, apparently. French ambassador Commynes formally protested the fact that pope wanted to strip the French king of his title of "Most Christian King" and grant it to Ferdinand and Isabella. So, back it is to Catholic Monarchs. The titling matter was discussed in the Concistoro on December the 2nd 1496, with cardinals Costa, Piccolomini, and Carafa acting as proponents. There were some protests in that debate, with some cardinals arguing that "Catholic is a title belonging to the Pope and to spiritual matters, not to secular people". There were also some protests coming from the Portuguese sector, as the title would have been "Catholici Reges Hispaniarum" (Catholic Monarchs of the Spains), when Isabella and Ferdinand did not rule over the whole of the Spains, as they lacked part of the Roman province of Lusitania and part of the Hispania Citerior.
Furthermore, as explained by cardinal Carvajal, the title of Catholic was granted in imitation "of your royal ancestor Alfonso the Catholic", a monarch from the 8th century, king of Asturias, a small kingdom quite noticeable far from the ambitions of a universal monarch, but definitely a catholic one in opposition to the muslims that dominated nearly the whole Iberian peninsula at that point