Republicans would need control of at least 34 state legislatures to be able to call such a convention, and 37 to ratify any amendments.
So far they have unified control of 31 state legislatures. Of those 31, 19 have signed onto an application for an Article V Convention put forward by Convention of States, a conservative activist group.
https://www.businessinsider.com/constitutional-convention-conservative-scholar-states-2022-8
https://www.businessinsider.com/constitutional-convention-conservatives-republicans-constitution-supreme-court-2022-7
A quick look at historical election maps on 270towin just shows how volatile political control of the states can be. There's no particular reason to think that Republicans couldn't engineer wave that would sweep through enough states to trigger a constitutional convention.
It's very sobering and upsetting wrestling with the reality that "progress" and "The arc of history bends towards justice" and similar sentiments are just some bullshit people made up, and there's actually nothing except some very mortal and fragile people standing between any kind of stable and peaceful life and absolutely horrific depravity. And historically we mostly lose that fight sooner or later.
It's interesting that MLK said the whole "arc of history" thing. He of all people understood how justice doesn't just happen, it's something fought for.
Kind of weird for him to pull out the whig historiography when he of all people knew how historically wrong it was. Like chattel slavery died out with the Roman Empire and then got brought back by bloodthirsty Christians to fuck over West African people in particular. That long arc of history most certainly did not bend towards justice.
If you think you can win your struggle, it helps to tell people that victory is inevitable. To quote Eugene Debs, "You can accelerate [socialist revolution] or removed it, but you cannot avoid it."