Can't Open Plex Anymore

The icon in the task tray belongs to the Plex media server.
A double click on it should open your default web browser with the local Plex web app. (Unless you somehow don’t have a default web browser set. In which case you’ll want to bookmark http://127.0.0.1:32400/web )
See Important note about the Plex Web app - Local Network Access for an additional point.

The Plex Player for Windows is a separate app and is downloaded and installed separately. I’m just mentioning it because you have tagged this post with it.