Maybe I'm wrong but I get the distinct feeling that it's not that people start by reading Bellarmine or Cajetan, but rather they might do confirmation bias on two common sense intuitions that both make sense:
1. Billions of Catholics hold that Leo is the Pope, by all appearances it seems that he is, I take it at face value. It seems very unlikely that he isn't and the Church has been destitute all this time.
2. In any normal world, if my bishop or priest said they had become a Baptist or a Muslim, they would obviously inmediately stop being my priest or bishop, even if it took a few weeks for Rome to decree it. I don't see why the Pope would be any different.
Again, look for the "signs of the times" as Jesus said. Read the Scriptures.
If you do that, you will see that the evidence you provide actually contradicts what the Scriptures tell you to look for:
1. You say that billions of people recognizing Leo as the Pope is evidence of its truth, as if truth is determined by the majority.
But read Luke 18:8 "I say to you, that he will quickly revenge them. But yet the Son of man, when he cometh, shall he find, think you, faith on earth?" Compare to Matthew 24:37-39 "And as in the days of Noe, so shall also the coming of the Son of man be. For as in the days before the flood, they were eating and drinking, marrying and giving in marriage, even till that day in which Noe entered into the ark, And they knew not till the flood came, and took them all away; so also shall the coming of the Son of man be." Only Noah and his small family were saved. The majority, who laughed him to scorned perished.
The point is that the much, much smaller part of the whole will be saved. And those who are saved will not be those gladly participating in synodality and such nonsense. That is a "new gospel" and is anathema.
2. You say an open apostate or heretic would stop being your priest or bishop.
So does the False Prophet need to buy a billboard and announce that he has lost the Catholic Faith? That isn't going to happen. There is an active deception going on. The guy is not going to openly admit that he is a Baptist or a Muslim. He is going to claim that the new Catholic Faith allows things that contradict the traditional Apostolic teaching, such as saying all religions lead to God or that sodomite couples should be blessed.
You have to pay attention and compare the Apostolic Faith to the new Counterfeit Faith.