Controllers under subfolder

Remember that MY_ classes existed in the old CI versions because there were no namespaces.. Now in CI 4 you are able simply to create App/Controllers/Controller and to use it from your other controllers..
The era of MY_ logic is over.

The term of "MY_Controller" or "custom controller" is only example for controller extends to \CodeIgniter\Controller and it is intended to be extends for any controller that having common behaviour/task to be done before it executed or some method(like AdminController verify user role before give access to any users).

It should not be put inside the Libraries folder it's not a Library Class it's a Controller Class.

Yes, it not recommended to put inside libraries folder. The "custom controller" should be organize in one folder. And controllers folder should only contain controller visitable by user.

Keep calm.