In fact, that'd be almost as reasonable as modern commercial interests arguing against some kind of theory that proposed humans were impacting the climate of the planet...
Good question. I've never thought of astronomy as characterized by a constant stream of progress building mainly on the work of past astronomers; instead, I've seen it as more in line with the model of "technology advances, with ancillary benefits to all sorts of different fields including astronomy". For example, radio telescopes owe a lot to progress in physics, but not very much to progress in astronomy specifically.
If that's the case, "none" is a very plausible answer to your question.
But the anwser to your question, "How many decades of astronomical progress did we lose to Urban VII?", given the sources referenced upthread is: apparently zero. Neither Urban VIII nor the rest of papacy seem to have held back Kepler or Newton.
It would have been surprising if the papacy were able to hold back Kepler and Newton, since they both lived in Protestant lands. That might be a coincidence. But maybe there were potential Keplers and Newtons living in Rome, or Madrid, or Tuscany, or even Paris¹, who were simply intimidated out of doing research.
¹ Even if they were Huguenots, who were still experiencing religious assassinations at the time, despite Henry IV; but especially if they were Catholics whose friends and family might suspect them of Huguenot sympathies.
That is very, very true. That PR fuckup carried on to this day and age. Three and a half centuries later, people still blame them for that.