I may or may not have a solution. But in my experience, between Android 13 and 15, the 3-button navigation bar became more "smart" and\or more complicated. 15 introduced Predictive Back which is on by default. 15 can add more static buttons onto the bar (Accessibility shortcuts, Keyboards). In 15 now my web browsers (Vivaldi and Firefox Beta) does not recognize "holding down back button" to show a recently visited webpage list. I am using Nova launcher on both 13 and 15 and I'm not necessarily getting 3-button navigation bar lag, but I am noticing windows animation intricities on 15, which Ive kinda fixed by slowing animations in the Developer Options.
The more 15 options I can turn off and make the 3-button Navigation Bar act "less smart" the more responsive it acts.