See a source on this at https://www.looper.com/752130/the-theory-that-connects-shakespeare-to-the-curse-of-oak-island/
Source suggests that the mystery associate with treasure hunters on TV series is about discovering a lost Shakespeare manuscript. Only link I see them dig up is a bit of old paper with a discernable "V" on it. And who/why would such a treasure be buried on Oak Island deep underground? Some ancient mariner wrapped his lunch it one?
On the other hand, reading Tempest with imagination does seem to square with an Oak Island in terms of mysterious island off the coast, treasure hunting, and Prospero at last burying his magic book, after dealing with personal conflicts, relatives, and going home again.