I want to be able to subtract from a mask any other masks I have previously created

"it seems to work only with brush-type masks, while object-type selection has "copy" disabled."

Interesting, Copy is disabled for all the AI mask components (Object, Subject, Background, Sky, People) but not non-AI components (Brush, Linear Gradient, etc.).  

But instead of doing Copy, right-click the component and do Duplicate, drag that component into the mask from which you want to subtract it, right-click the component, and do Subtract.

That you can duplicate but not copy AI components seems like a bug to me, but Adobe will probably consider it "as designed".

"this is not a solution. Not only it is very cumbersome ... I want to be able to select the whole mask, consisting of several brushes, objects, etc."

It's a solution but obviously one that involves more steps and is significantly less convenient. You can duplicate and subtract each of the components in the mask from the target mask.