No matter how many political ballots were burned to select him, the Pope had no more business issuing edicts on natural matters like celestial mechanics than the politician-appointed SCOTUS had in declaring CO2 a pollutant. Both were acting outside their respective spheres of expertise and authority.
The Pope never issued an edict on celestial mechanics and as I stated previously, the Vatican, probably lead by the Jesuits who were crytpoheliocentrists, explicitly avoided the controversy. There were forces in the Vatican working to reconcile Catholic doctrine with heliocentricism. They saw Galileo as bull in a china shop. They knew the arguments and mathematics of heliocentricism better than he did, but they wanted to advance the ideas without creating any unnecessary confrontations and without confusing the laity. Martin Luther was on the record as condemning heliocentricism as sinful heresy, while the Vatican never spoke on the issue.
Galileo just had a way of making enemies and playing martyr for science. I suppose by forcing the issue he did manage to embarrass the Church for going on half a millennium. The Church never really requited his bile. He was treaty humanely while in house arrest and the Vatican has since cleared him. What he did may be seen as suffering for advancement of Truth and Science, but others see it as rank egotism and arrogance, which harmed an institution and individuals that had treated him very well.