There is no formal “next in line”. The closest potential successor would have been the deputy prime minister; Chrystia Freeland held that role until a few weeks ago when she dramatically resigned and sparked this chain of events.
Currently, this is “Working as Intended” in Canada’s political system.
Usually what happens when a party is not in power is that the leader will resign and an interim leader will be appointed until a new leader is elected through a leadership election. When a party is in power however, that interim leader would be an "interim Prime Minister" and is avoided because it's a lot of responsibility to give to an interim with no mandate from voters or the party.
There is no such thing as a "vice-PM" in Canada. There is no "next person in line", and parties choose leaders more or less independently of the election cycle, according to the party's needs.
The Governor General appoints a caretaker government with (ostensibly) limited powers until the party in power or the leading coalition select the next PM and create a new government.
Absolutely not. Just like every developed country, there is a continuity plan in case of issues. The deputy leader of the party in power is supposedly that person. That the Governor General then appoints that person Prime Minister is an implementation detail.
It's just that in Canada, that continuity plan is reserved for unfortunate deaths. When a PM wants to resign, they basically do what Trudeau did; they announce their party will do a leadership race while they stay on as PM.
The nuance here is that the Governor General by convention follows the advice of the PM, who establishes their continuity plan at the start of their government (IIRC it’s a standard party document and they just update the names).
It’d cause a crisis with the monarchy but they’re not legally bound to appoint the deputy. Like you said it only applies to special circumstances, I was just addressing the legal mechanism by which it happens (as the OP talked about a PM dropping dead).
In the Westminster system, being bound by tradition and being bound by law (written law that is) both have the same legal weight. Our courts can render decision on the necessity of following tradition.
