input_delay doesn't seem to address this in general: Even when set to 50 (which is very noticeable), the cursor on the next line just appears with some delay.
Interesting, In zsh I experienced the exact behavior you described and setting input_delay to 10 completely resolved it. To be fair, when testing my PS1 was simply '%m$ '.
I just benchmarked 'starship prompt' and when in a directory managed by git, it can take well over 10ms. I imagine with a more advanced configuration it would take even longer. urxvt must be doing something special.
