Hi, MJak8.
It sounds like you’re familiar with listening to your Shazam tracks in the Music app on your iPhone, but you’d also like to listen on your Mac.
Since you’re an Apple Music subscriber, songs that you Shazam should be automatically added to a playlist in called My Shazam Tracks in the Music app. Do you see it on your iPhone? If you’re not seeing this playlist, you may need to sync your music library.
Turn on Sync Library with Apple Music - Apple Support
If you see the playlist on your iPhone, make sure you’re signed into the same Apple ID on your Mac. Use the same article to sync your music on your Mac, and check for the playlist in the Music app on your computer. It should sync across devices with your Apple Music subscription.
This article explains:
Use Shazam with Apple Music, Snapchat, and more - Apple Support
We appreciate you taking the time to post in the Apple Support Communities.
Warmest Regards.