C++ classes can appear in the content browser, but are not considered “content”. Yes, a very confusing usage of terminology by the Editor.
In the content browser, you should see the word “Content” in bold with a folder icon to the left and a triangle to the right. Click the folder icon and select “C++ classes”, then click the name of your project. You should then be able to drag the class into the level (if it inherits from Actor).
It’s unfortunate that C++ classes do not show up in the default view.