No, Kim Campbell, the sitting Prime Minister ran in the election.It’s much more complicated than “he’s in a minority therefore he’s running” in this situation. He can step down at anytime and pass the reins when ever he so chooses given his current arrangement. That is exactly how it can work.
Can his deal be scuttled and we end up in an election he has to run in? Sure. But the NDP are far too comfortable with this deal. Trudeau wanted a majority to cement his legacy. He tried and Canadians refused to give it to him so he has the next best thing. He’s in a minority situation and able to govern as a majority.
I won’t repeat ad nauseam again why I think he won’t run. But I could see an announcement in early 2023 and either a coronation or a one sided short leadership campaign. Then the new leader arranges an engineered election “ie the new leader wants a new mandate or something like that” but not before he or she has had time to make their name known enough and that the conditions are right.
Your last point is noted though. But trudeau wouldn’t have to be the sitting PM at that time. Brian Mulroney stepped down and didn’t run. I’m sure that Trudeau would be more than happy to remain undefeated.
But, this is just theory crafting at this point in my part. If I get it wrong I get it wrong.