I will explain how to interpret symplectic Morita equivalence as an equivalence of fibered categories. This will allow us to view symplectic Morita equivalence as equivalences of geometric stacks over the site of Dirac manifolds.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/3946