Well, something happened! I finally got an answer to the case I reported using the feedback assistant on October 19th, 2022 (and then repeatedly updated with every iOS update).
They sent me a long text asking me to install 2 iOS device profiles, "UI_Hang_Diagnostics" and "PerformanceTrace", along with some instructions on how to capture those traces and send them to Apple when the stutter happens. It's quite convoluted and it will be a hassle to reproduce consistently, but I will gladly do that effort so we can finally get rid of this pesky issue.