Why there is no quit button in GarageBand for Mac?

The red button is present on my Garageband (Catalina):

The red button is not a Quit button and never has been. In all applications the orange button mimizes the window, and any processes which are running within it continue. The red button closes the window, so that any processes stop, but the actual app continues to run in most cases. In some simpler apps closing the last open window also quits the app.

My version of Garageband brings up another window for creating a new project when you click the red button. Safari on Catalina does not quit or bring up any window when you click the red button to close the window, and neither does Mail.

In the case of an application like Safari which can have multiple windows open you can close (rather than minimize) one window and leave the others open, so you certainly don't want the app quitting when you click the red button.

Best to send your suggestions directly > Product Feedback - Apple

Pending any potential changes, Command-H and Command-Q. Mac keyboard shortcuts - Apple Support

Mine has all three buttons. Are you in full screen mode?

The are greyed out here because of the screenshot, if you hover over them they show up in all their glory.

A very good rhetorical question. It has been this way in all versions of GarageBand I have ever used, even in the older iLIfe versions. Closing the window will prompt us to open another project. It useful, if we want to copy and paste tracks between projects. I am not using this feature very often, but sometimes it will come in handy.