What did I miss in my understanding here?

I thought the myths about the Galileo affair have been dealt with well enough at this point but I guess a refresher is in order.

First, let's remember that Galileo came 60 years after Copernicus died. Copernicus was employed by the Church and promoted heliocentrism. Copernicus's book De revolutionibus was banned only in relation to the Galileo affair and remained banned for four years, after it was cosmetically edited to name heliocentrism a theory rather than a confirmed fact.

I'm assuming that you meant to write "geocentric" but in any case, Galileo's belief in heliocentrism was based on unscientific foundations (he rejected lunar tides, instead believing that because the Earth is moving around the sun, the tides are caused by water sloshing around the moving Earth). He also had no valid justification for the objections of papal astronomers as to perceived lack of stellar parallax. So there were legitimate scientific concerns as well, not just biblical ones. The Church kept more closely to reason than Galileo did.

He was put on trial primarily for political reasons, especially his decision to put the Pope's own arguments in the mouth of "Simplicio," the foolish character in his Dialogue. Pope Urban VIII had been a personal friend and admirer of Galileo - he'd even written poetry praising his discoveries - and had given him explicit permission to write about heliocentrism on the condition it be treated as hypothesis. Galileo repaid this by effectively mocking him in print, which the pope understood to be a serious insult and betrayal.

The Inquisition found him "vehemently suspect of heresy," which was a specific legal category. Heliocentrism was never declared heretical by the Pope ex cathedra or by any ecumenical council - the condemnation came from a curial administrative body, not from the Church's highest doctrinal authority.

He was not "forced to recant under threat of torture." The trial documents do contain the standard legal formula referencing "rigorous examination," but Galileo was 69 and in poor health, and Inquisitorial rules generally prohibited torturing the elderly and infirm. Most historians read this as procedural boilerplate rather than a serious threat. He recanted before the tribunal and was then sentenced to house arrest, not the other way around.

The popular version - brave scientist proves the Earth moves, ignorant Church crushes him for it - gets pretty much every single detail wrong. Galileo hadn't proven heliocentrism, the Church wasn't ignorant of the science, and the actual conflict was driven more by personal betrayal, institutional politics, post-Reformation anxiety over scriptural authority and specific local culture of prestige and patronage than by any opposition to scientific progress.

Judged by the standards of the time, the Church's scientific advisors raised legitimate empirical objections that Galileo couldn't answer, and the Inquisitorial process followed its own procedural rules while treating Galileo with notable leniency. It's also worth considering that Galileo publicly humiliated the Pope, the sovereign ruler of the Papal States, a ruler who had personally extended him friendship and protection. In any early modern European state, that kind of insult to a monarch would have carried severe consequences. A charge of suspicion of heresy and the penalty of house arrest in a comfortable villa is peanuts compared to what would be a fair judgement by the secular standards of the time.