Should I report a PhD student’s incompetence to their supervisor?
Emailing the supervisor and saying "this student is incompetent and you should get rid of him/her" would come across badly, for a few reasons:


You lack the information to make a holistic assessment of the student.
Even if you're right and the student is weak, weak students can improve.
The supervisor and their institution undoubtedly have their own methods of quality control.
Most importantly, it's not really any of your business.


It's nice that you made a good faith effort to answer the student's questions, but if the exchange has become annoying for you, your best recourse is to simply stop responding and forget the student exists.