Do Shia believe Nahj al-Balagha is completely authentic the same way Sunnis believe sahih Bukhari is? If so, how does one explain the sermons found in it attributed to Imam Ali (a) that claim women are intellectually deficient etc? That’s contradictory with the whole spirit of the Quran where Allah states that man and women are equal in deed.

Also, how can any work that isn’t the holy Quran be considered 100% authentic?

Nahjul Balaghah and other books of tradition are not entirely authentic. As you mentioned, only the Holy Quran is.