As per the actual message… you get to see this while the server is processing the update. In this particular case, the upgrade to PMS 1.40.0 contains a significant amount of updates to the database structure. Depending on the size of your database and how powerful you server is, this might take a moment.
My server completely disappeared after the upgrade. The plex.tv connection is stuck on connecting. And hitting it directly on 32400 doesn’t load either.
Just installed on a QNAP. It’s been “Plex Media Server is currently running startup maintenance tasks” for the last 20 minutes. I guess I’ll wait overnight and then restart the server.