What are the module categories over the modular tensor category **Fib** of Fibonacci anyons?

By Ostrik's work, we know these module categories correspond to separable algebras in **Fib**. I do not believe such things have been classified.

Davydov and Booker show there are no nontrivial *commutative* separable algebras in **Fib**, but I do not see that they make a clear statement for this more general case, without commutativity.

My guess is that there are indeed no nontrivial module categories for **Fib**.