I can't see an issue here, what precisely do you mean by you "can't"? You should see a list of modules and when you click the module, a plus icon to the right. Are you using an admin or non-admin account?

I attached a screenshot.
If I select an available class from the shown list by , I'd expect that it would be added to the included classes.
However nothing happens.

If you click on any of those blue "shared-*" headings, it should expand like my attachment, changes the "+" to a "-" and then shows a list of classes in black underneath. What happens if you click it?

If that isn't working, try opening your browser console (usually Ctrl+Shift+J) and try it again, paste/attach any messages from the console to this bug report along with the browser version, in case it's an error there.

Is this an upgrade or a clean installation?

Something looks wrong with how the page is rendering, probably a missing JavaScript file. On the Sources tab of your console you should see a class_edit.js file, did that download OK? It should contain expandClassList. (See attachment.) If not, the network tab may show an error?

Possibly the assets weren't recompiled successfully, that's the bundle exec rake assets:precompile line.

Anyway, glad you sorted it!