Is there a keyboard shortcut to favourite a song in Apple Music on Mac?

Short answer: no. Apple's list of Music keyboard shortcuts has shortcuts for playing, skipping and showing the current song in the list, but none for Favourite

Why you cannot assign one yourself

The usual trick is to give a menu item a shortcut in System Settings → Keyboard → Keyboard Shortcuts → App Shortcuts. It needs a menu item with the exact title. In Music on macOS 15 we listed the items of the Song menu and searched all menus for Favourite, Love and Like. There is no such item. Favourite lives in the More menu and on the favourite button, which App Shortcuts cannot reach

What works

1. The button. Point at the song, click the favourite button, or open More and choose Favourite. Apple's guide describes this route. It needs the Music window
2. A script on your own shortcut. One line of AppleScript sets the flag, and a launcher or the Shortcuts app on your Mac can run it from a key combination:

tell application "Music" to set favorited of current track to true

The script and its caveats for radio and streaming songs are in how to favourite the current song with AppleScript

1. One right click in the menu bar. Likeit puts a star in the menu bar: right-click it and the current song becomes a favourite, right-click again to remove it. It works while Music is in the background

A shortcut you did not ask for

One Apple Community user reported that with Keyboard navigation turned on in the keyboard settings, pressing Space to pause a song also favourited it. We have not tested this. If songs get favourited by accident, check that setting first

Which one

If you favourite songs now and then, the button is enough. If you want a key combination without opening Music, use a script. If you would rather click once and see the state, use the menu bar star