Yes and no. Yes, iPhones get throttled when the battery is on the verge of going ex, but no for this particular device. I run an iPhone X with a new battery from November 2021 (serviced by Apple), with maximum capacity at 90%, and it really is slower compared to the old days.
But!
I'm not complaining. It's an almost 6 year old device. That means, for every year of usage, I payed roughly 200€, or 16€ per month. That's not too shabby, tbh.