Will the same assignment show up twice if it's in Canvas and my calendar?
No. Secretariat keeps one to-do per piece of work: when Canvas, your syllabus, your calendar or a to-do app list the same thing, they're folded into one, and checking it off checks off all of them.
How it decides
Plain rules, no AI, on every sync. It matches names and numbers, so "Pset 5" in one place and "Problem Set 5" in another are one to-do, while two different things from one class stay apart. To-dos you typed in yourself are never folded into anything.
Nothing is lost
The to-do's details say what was folded in and from where, with the other date if it gave one. If two things really are different, tap Show separately and they stay apart for good.
The same calendar twice
If you add a second link to a calendar that's already connected, Secretariat tells you it's the same calendar instead of doubling everything.