I am not sure.
I think the inflation was mainly caused by two things neither of which is curable with interest rate rises: the aftermath of the pandemic during which supply chains were in bad shape and rents rose due to WFH; and the massive but brief increase in energy prices due to Putin's war.
I suspect both are resolving themselves and that interest rates merely appear to have had an impact because that's the tool central banks have been applying.
Maybe the rises helped quell demand some by saddling folks with horrific mortgage rate increases. But the risk is they have misidentified the actual cure while really just harming the patient.