Not specific to accents, but a burlesque accent is a possible term. Definitions include “A ludicrous or mocking imitation” and (in other dictionaries) “intentionally broad for comedic effect”.
PS- Channel surfing an hour ago I came across the Steve Martin version of Father of the Bride in which Martin Short (as “Fraunk”) has this type of accent.
Whatever it is, she talked exactly the same way when she appeared in a Babylon 5 episode as the Centauri seeress Lady Morella. (BTW, y’ever notice that not one other Centauri talks like Londo Mollari?)