If you’re refinancing the debt you have to pay the higher rates, which is why I mentioned the fact that the U.S. apparently needs to refinance something like $9trn/one quarter of their $37trn debt this year. Just a 0.5% increase equates to around $50bn extra a year interest. A lot of this debt was taken out at far lower rates so the spike in debt servicing costs for US (and ourselves/others) is eye watering.
You’re correct it makes no difference to the amount of interest paid on debt already taken out