Interesting question!

Alexander VI was Pope from 1492-1503. Innocent VIII was Pope from 1484-1492, so it was Innocent who oversaw the transition between Richard and Henry and the Battle of Bosworth.

Henry VII maintained a good relationship with the Papacy throughout his reign, being as devout a Catholic as his mother. Henry was quick to swear loyalty to the Papacy - not wanting (nor desiring in this case) to make waves - and in return Innocent recognised Henry as the rightful King of England and gave dispensation for his marriage to Elizabeth of York (they were cousins to some degree). Innocent also will have been keen to make an ally of the English, and everyone they could, as the Papacy had recently come into conflict with Naples.

This positive relationship with the Papacy continued into Alexander VI (the Borgia Pope, as I’m sure you know)’s Pontificate. The first Italian War began in 1494, and Henry VII officially sided with the Holy League (also known as the Anti-French League), which, predictably from the name, was in defence of the Papal States. Whilst Henry was technically allied with them, he never sent a single troop, penny, nor anything else in their aid unless they traded for it. At the same time, he made a trade deal with France. Neither side in the first Italian War wanted him, it was simply that neither side wanted him to join the other. As such, his relationship with France improved and remained the same with Borgia.

After this, Henry withdrew from foreign policy, including with Rome (and from domestic policy, Parliament, and government in general) due to his declining mental and physical health after the very rapid deaths of his second-favourite advisor, eldest son, wife, and favourite advisor. Henry did not join the second nor third Italian Wars for this reason, and as such his relationship with Rome (and the rest of Europe) stagnated - though it did not drop off by any means. This is shown in December 1503 when Julius II gave a dispensation for Henry’s son, the future Henry VIII, to marry Catherine of Aragon; she was previously married to Henry’s older brother, Arthur Tudor, who died in 1502.

By 1509, King Henry was incapable of government, and had been largely forgotten by most of Europe. However, one of his last wishes was for 10,000 masses to be said for his soul - and as such there is no reason to believe that the Papacy ever had a negative view of him. They readily accepted Henry VIII as King, with Leo X actually gifting him a Papal Sword, which was one of the highest honours a King could receive from the Pope, in 1513. Obviously, and rather famously, that positive relationship ended in the 1530s.

So, in short, yes! There was support for Henry VII’s reign from the Papacy, and it was significant in his early years; his reign would have been much weaker without the Papal dispensation for his marriage; this marriage is what placated many Yorkist supporters to his reign, and the dispensation for Catherine was a large sign of goodwill from Julius for the ailing King, as it contentiously gave great security to Henry VIII. This dispensation is a large part of what caused the Reformation. There was never any ill will between the Papacy and the Tudors from 1485-1530ish.

Hope that gives an adequate answer to your question! Happy to give any more information/answer any more questions about Henry VII of England. He’s possibly my favourite historical figure.