i don't have any big thoughts about Brecht himself, as my knowledge is mainly couched around his interest in Shakespeare. but you are correct to discern that Brecht sees in the early modern theater an avenue for the development of his own dramaturgy. one part of this that matches up pretty well is Brecht recognizing that many early modern historical plays (or otherwise) are often written in ways that make commentary on their contemporary political developments (staging "history" was a way to get around scandals and censors). he follows suit in this, writing stories that work as fables and as political polemics. the thing i tend to bring up more often is probably the rickety nature of theatrical belief, which plays of Shakespeare's time are constantly trying to shore up or incite. this is where the distinctions matter; a simple reading of early modern plays would see them grasping toward an audience that accepts their fictions with little prompting, ie, a naturalized docility in the theatrical spectator, whereas Brecht is taking cues from archaic theatrical practices or less formal popular entertainments in order to undo that precise spectatorial mode.
