Google Play Music will begin shutting down in September

Helpful of them to put "Google" in the name so that you know in advance that it will be cancelled soon.

I use the Play Music app to play music stored locally on my phone's SD card since the app came with the phone. Does Youtube Music also have this functionality, or is it just for their streaming service?

I moved to Deezer. YouTube music was not an improvement on Google Play music. At least now I can get better quality audio