iMac set to use cloud library only and not locally stored music

There is no switch you can flip to make the Mac use the songs from the cloud. It does not work that way, and it's not recommended. The iCloud Music library is not a backup. If you delete a song from your library it will delete it from the iCloud music library too and all other devices.

The Mac is the basis for the iCloud Music library and any changes to it will affect the iCloud library.

There are many posts here about people losing their entire library from the cloud and being unable to recover it.

The best you can do, and should do, is backup your library to an external hard drive, and then open a new empty library on the Mac.

It will then have nothing and stream everything from the cloud, but your existing library will be safe on another drive.

click here ➜ Move your iTunes library to a new drive or computer - Apple Community

Then shutdown the Music App, open a Finder window, go to the Applications folder, hold down the option key, and double click on the Music app there to open it. It will ask you to Choose a Library or Create a Library. click on "Create a Library".

It will create a new empty library in a location you determine. Make sure you are logged in with your Apple Account, and turn on Sync Library to access your iCloud music library without downloading the songs.