Please note that opening Plex does not reveal a UI. Plex Media Server runs in the background. To check if it is running, look for the Plex icon in your system tray (the area with icons in the bottom right next to the clock). You manage PMS using Plex Web, which you can open manually if you know the URL, or you can right click on on that PMS icon and then select “Open Plex…”
Edit - To add, you logs look fine. PMS appears to be up and running.
