Hi there. Plex user here. Their media server is NOT on the App Store, let's get that out of the way. in fact, their player isn't on the Mac App Store either. It IS on the App Store for iOS/iPad OS, but you shouldn't be trying to install that even on an M1 Mac.
If you do indeed want the Plex SERVER (in other words, you want to HOST your media library), then the link Raz0rEdge provided is the correct one. What you MAY be seeing is a consequence of only allowing apps from the App Store to run. You can right-click on the app and then select "Open" to bypass your security settings. You'll get a prompt asking if you really want to do that.
Now, if you want to just PLAY media, which would require access to a server hosted by either yourself or someone else, then you need the Player, not the Server. However, you can PLAY via the Server if you host your media on the same Mac. Here's that link:
Click here to Download the Plex media server for Windows, Mac, Linux FreeBSD and more free today.
www.plex.tv