The word "mentee" is of recent vintage, according to Merriam-Webster. It appears to modify the word "mentor" when no such modification is necessary. Read the dictionary definition of "mentor." The word originates with a Greek character and defines a teacher. Read the dictionary definition of "protege." It originates from French and defines a learner. Read the Wikipedia description of mentorship. It clearly describes the relationship between mentors and proteges. There is no need to create a new word for protege that modifies the word mentor.
I prefer to use traditional language. I lament such changes to the English business lexicon. Calling someone a protege worked perfectly fine for a long time until some writers decided not to pay attention anymore. I have mentored people in the past and may do so again. I do not need to be anyone's protege; if I were for some reason, I would never call myself a mentee.