Is my old PSU holding back my new RTX 4070 Ti Super performance?

I just upgraded to an RTX 4070 Ti Super, but I'm getting lower benchmarks than expected and occasional stutters in demanding games. My current PSU is an 8-year-old Corsair RM750x. Could this aging power supply be the bottleneck, or should I be looking at other components? Really curious if a new PSU would make a noticeable difference.