Gonna reply to myself and say that I literally just found a solution to this issue after WEEKS of trying to figure it out, thanks to another similar post I found on this forum: Scaling Factor Issue Seems to be Back in Windows 1.8.0.1159-67c4a549
One of the comments suggested setting an environment variable so Qt could know what to do, and I thought Hmm, I might as well try that and see if it changes anything. To my surprise, I opened my local environment variables and found one already set called QT_AUTO_SCREEN_SCALE_FACTOR that was set to 0, probably there from some other Qt application I was using before I got the second 4k monitor.
Long story short, I removed all of the Qt-related environment variables, restarted, and now the Plex app is displaying 100% fine on both screens. I can’t believe it took me this long to troubleshoot it myself, only to open a post and discover within half an hour that it wasn’t a problem with the app at all.