do i need to save my music on my pc?

Good day Vallouise,

Apple Music does indeed allow you to keep your music in the cloud, available to all your devices with an Internet connection without having to store it on those devices. See this article - About Apple Music - Apple Support

It should be noted, however, that Apple Music is not a backup. Specifically -

Back up your music

Back up your iOS devices, and your Mac or PC, so that you have a copy of your music and other information if your device is ever replaced, lost, or damaged.

Apple Music doesn't include a backup service, so make sure that you always have a backup of your music collection.

Thanks for using Apple Support Communities.

Safe computing.