The unmistakable voice of H. John Benjamin (Bob’s Burgers, Archer) appeared in the Short Trek: The Trouble with Edward. Seems he’s the one responsible for the “ecological menace” of tribble proliferation. Don’t know if it’s considered canon, but I can live with it.
I say Short Treks is just as canon as Discovery. Whether or not you consider Discovery “canon” is up to each individual, but if you consider that show canon, you should consider Short Treks canon as well.
The episode is canon. The tribbles cereal commercials… maybe not.