Then there is no wonder why the plex web app (which has been loaded from app.plex.tv) has now trouble communicating directly with your plex server on your local network.
Enter the settings of Chrome - Privacy & Security - Site Settings
if app.plex.tv is not listed there, click on “View Permissions and data stored across sites”
use the search box to filter for plex.tv
Click on app.plex.tv
scroll down and set “Local network access” to “Allow”.