Thanks for checking those settings and getting back to us, Nick. It's appreciated. Since this is happening on two separate devices on two different operating systems, I'd like to make sure that your devices are up to date.
Update your iPhone, iPad, or iPod touch -- iOS is currently on iOS 13.4.1.
How to update the software on your Mac -- macOS 10.15.4 is the latest for your Mac.
If either require an update, please be sure to have a fresh backup to keep your personal information safe.
How to back up your iPhone, iPad, and iPod touch
Back up your Mac with Time Machine
Apple - Support - Product Selection — If you still can't add song to your Apple Music library to either device, please contact Apple Support. After selecting this link, choose Music, Apps & Services > Apple Music > Saving & Playing songs. The select how you'd like to start the conversation.
Cheers!