When it comes to Canadians working in the US on a TN, are we allowed to accept promotions (title, comp or both) without going through reapproval of our visa? Are there any nuances here like caps on how high a salary increase could be before needing a reassessment? Maybe increases in equity don’t count?

Also if the reassessment is denied does your original visa still remain valid or are you risking it all for the promotion?

There's a lot more flexibility in the TN context than in the H-1B context so generally it's not an issue to get an inline promotion as long as the core job duties remain the same as or similar to the job duties in the initial application.

IANAL but I had TN status. AFAIK there is no issue as long as your profession didn't change.