Update 1 (08/06/2020 @ 05:40 PM ET): One big issue with the upcoming shutdown of Google Play Music will be how it affects Wear OS, as there won't be a YouTube Music app to replace it. Scroll to the bottom for more information. The article as published on August 4, 2020, is preserved below.
For those of you who still love and use Google Play Music, I'm sure you've heard of this news by now...but Google is killing off the service and replacing it with YouTube Music. Since YouTube Music launched in 2018, both it and Play Music have coexisted even though Play Music was no longer in active development. Google slowly added new features to YouTube Music to convince people to migrate from Play Music, and more recently, introduced a migration tool to transfer your songs, albums, and playlists. The goal was to get people to fully migrate to YouTube Music so that Google can shut down Play Music. That day will soon arrive: Google Play Music is shutting down for everyone by December 2020.
According to the official YouTube blog post on the matter, the final stage of Play Music's shutdown will go pretty quickly. Starting in September in New Zealand and South Africa and October for the rest of the world, you won't be able to use Play Music anymore. This means that you won't be able to stream from the app or, well, use the app at all. Google will, however, still hold onto your Play Music data until December so you still have time to migrate all your uploads, playlists, and purchases over to YouTube Music, or if you have any podcasts, to Google Podcasts. After December, however, the service will be killed off once and for all.
The other way you can save your content is to use Google Takeout to download all your purchased and uploaded content. Google will notify you before you lose access to what's on your Play Music account, but be mindful that you only have a few months left before all of it is gone forever.
On the bright side, Google has already built most of Play Music's features into YouTube Music, so after migrating, most users won't miss much. Google Play Music is dead, long live YouTube Music. (Feel free to vent in the comment section if you need to, though.)
Update 1: No YouTube Music App for Wear OS
On a support page (via AndroidPolice), Google Community Manager Zak P states that the Google Play Music app for Wear OS smartwatches will be shut down "in the next couple of weeks." When it's shut down, there won't be a replacement app like there is for regular Android devices, though. Google has yet to publish a dedicated YouTube Music app for Wear OS, so the company is telling users they'll have to instead control music playback from their smartphones. That hurts Google's claims that the migration from Play Music will be seamless for all users, as it's evident that the process will leave Wear OS users with reduced functionality. The Play Music app for Wear OS, for example, allowed for local music playback, which when paired with an external Bluetooth audio accessory, allowed you to fully untether your music playback from your smartphone.