The influence of St Thomas Aquinas, Pope John and the Malleus Malificarum is not imo a 'nothing burger' in the world of the state killing women in the western tradition.

I don't know about Thomas Aquinas*, but Pope John only said that witchcraft could and should be tried by the Church. Therefore, the damage he caused could be estimated by how many "witches" the Church killed, and the answer to that is "not many." Like I said, the vast majority of witch trials were done by secular courts, and Church (inquisition) courts were much more likely to hand innocent verdicts or lenient sentences. The Malleus Malificarum was definitely a problem (though certainly not the problem; the period where most executions happened started more than 70 years after it got published), but the Church never endorsed it or otherwise used it to my knowledge.

*I gave up and looked him up, see below but that's absolutely a nothing burger.

I'd be wary of history via wikipedia but if you are doing that Italy, where Aquinas was from, might be worth a peek for the 1300's to 1500 or so period: https://en.wikipedia.org/wiki/Witch_trials_in_Italy

I did, and... the same pattern holds?

The Inquisition did not consider witchcraft a priority compared to heresy, particularly after the introduction of the Counter-Reformation. It maintained the policy that the Witches' Sabbath was an illusion caused by Satan rather than real, and did not accept a charge of witchcraft based solely on the testimony of an already charged person.[4] As in the case of heresy, people who were condemned guilty of witchcraft by the Inquisition, and repented, were not executed the first time they were condemned, only if they relapsed and repeated the crime, which also contrasted with the secular courts.

Most witch trials in Italy were conducted by local secular courts and not by the Inquisition.

Again, the Church had little to no role in any of this.

1300-1517 we have hundreds of women being killed as witches with the RCC from Aquinas to 1620 throwing petrol on the fire.

Adding to what I said above, this is all in Italy. We have data points elsewhere: Spain and Portugal, both under strong Catholic control, saw very few witch trials during this or any other period specifically because local inquisitions were the ones running the trials.

While it's tempting to just ignore the machine that started burning women alive using idiotic theology to prop it up for hundreds of years and instead focus upon when it went hysterically viral I think it's worth remembering who laid the groundwork.

Even if we accept the (very inconsequential) positions taken by select Catholic leaders as "the groundwork," I don't think people should be judged for the actions of people who claim to agree with them. Both Aquinas's work and John's papal bull would need to be quite a bit more misogynistic and murderous before we can assign either man blame for this. I mean hell neither of them even mention women in their relevant statements. By this logic we could blame Adam Smith for the Irish Famine.