I reported this issue to the email address provided on the Play Store page for the Plex Android app, and they sent me an automatic response to come here. So let me see if anyone else in the community has my issue.
Whenever I cast a movie or show to my Chromecast from my Pixel 3 XL, the playback Screen is completely shifted up. See the screenshot for a reference. The rest of the app seems to be compatible with the display cutout (the infamous notch).