DR George, Aristophanes' plays are neither sequels nor prequels, although if more existed, scholars might change their minds. All were satirical or political comedies about aspects of Athenian life and the endless Peloponnesian War, and my favorite remains the bawdy, obscene, anti-war Lysistrata. So The Birds, like Peace, The Clouds, The Wasps and others are not related to The Frogs.
Now, Vaughan Williams composed music for an Oxford production of The Wasps, which he turned into a concert suite, and Braunfels' opera The Birds was first performed in 1920. It has nothing to do with Sondheim.