A formal mechanism doesn't exist because it wouldn't be seen as democratic.
A similar scenario happened in Manitoba, where Selinger had the voters (well, NDP members) choose who to be leader. I think this is what Canadians would expect. Either the leader sees the writing on the wall and resigns, or puts it up to a vote of the membership (not the MPs/MLAs)
You are forgetting that in Canada party leaders have been toppled at party conventions when there has been a leadership review that didn't pass some imaginary threshold. In 1982 Joe Clark was toppled as PC leader when he only got 67% of his one party to support him. He then ran to succeed himself and lost. Similarly Ralph Klein quit as Premier and Alberta PC leader after he only got a 55% vote of confidence in a leadership review.
This is not the same thing. In those instances, it was party members doing. In Australia, it was just the caucus.
Yeah, the fact that the Prime Minister of the 15-ish world power can be toppled by nothing more than a vote among a bunch of a hundred of party apparatchiks is... unsettling, to say the least. Makes Australia look a bit sovietic, tbh, and not in the good sense of the word.