I went and saw Faust at a local theatre and was struck by Mephisto's design

That's a vampire! That is the classic old school cinema vampire. Long black cloak, slinking around the room, and the classic hair style. I was sure I was seeing the addition of the Widow's Peak to the vampire repertorie, even if Mephisto is not one himself.
But upon looking into it I found the claim that the style comes from the famous Bela Lugosi, and his actual hairstyle.

Article with the claim
But that article gives a year for the first appearance of Bela on stage as Dracula, 1927. Faust was released in 1926!
I have found one article making the same connection, so I'm not the first one to see this link
Janning’s cape and widow’s peak seem an obvious inspiration for Lugosi’s Dracula. This is also hinted at in his appearance over the village as a giant bat.
Blog Link
But Faust was not a commercial success, is it really believable that the Broadway version of Dracula was pulling so much inspiration from a German movie released just a year earlier?
I'd love to know if anyone can correct me on any of this, or has any information to resolve the mystery.
Also go watch Faust if you haven't, its a fantastic movie.