"Now my charms are all o'erthrown, / And what strength I have's mine own" (Epilogue). So says the newly retired magician as he bids adieu to the audience. Since The Tempest is likely the last play Shakespeare wrote by himself, the epilogue has long been cited as Shakespeare's own fond farewell to the stage. Regardless of whether or not we read Prospero the magician as a stand-in for Shakespeare the playwright, the similarities between Prospero's "art" and the "magic" of the theater are undeniable. Like Hamlet, The Tempest not only features a "play within the play" (Prospero's dazzling wedding masque) and blatant shout-outs to the theater, but it also features a protagonist who manipulates the play's action like a skillful director.
When Prospero uses his magic to produce a masque, or "some vanity of [his] art," the play makes it clear that the old magician is a lot like a master playwright.
It doesn't make any sense to associate a grumpy, revenge-thirsty magician like Prospero with a playwright like Will Shakespeare.