Raising interest rates to fight inflation works by reducing demand. Jobs get lost so people have less money. So they spend less, so prices drop to be more competitive.
Only poorer people obviously. Rich people are less affected, but still pay more in interest. The increased number of unemployed people means competition for jobs is higher so workers are cheaper to pay, increasing profits again.
High inflation is bad for everyone, but particularly so for the poorer, too. However, measures to fight it should be spread across society. Instead blunt tools like interest rate rises disproportionately affect the poor. They should be combined with higher taxes on business and high earners and high net worth individuals. Worldwide we only really do the first. I wonder who decides?