I mostly agree except for : "the governing Coalition Avenir Quebec = the Conservatives"
There's is no equivalent of the Conservatives party in Quebec politics (well actually there is but they only got 1.46% in the last election and are not recognize as an actual party by the National Assembly of Quebec) . The Conservatives are more akin the US Republican in regards to climate change, gun and gun control law, LGBTQ issues and abortion rights. There's is no parties in Quebec politics that does not fully believe climate change, that is hostile to LGBTQ rights, that is pro gun, or is against abortion. on the Left to right spectrum the Quebec Liberal party is even more on the Right than the CAQ (Coalition Avenir Quebec). Although, even Quebec Liberal party would actually be considered a Left (probably event far left) party in the US.
You're just factually wrong about this. I mean you say there's no point of comparison between the Coalition Avenir Quebec and the Conservative Party of Canada, and yet Quebec's premier, Francois Legault, who belongs to the Coalition, has very publicly endorsed the Conservative Party in this federal election:
I don't think points of comparison get more direct than endorsements. The question of Quebec sovereignty appears to be the main ideological difference between the two parties, in fact. To be sure, from the standpoint of advancing Quebec's independence from Canada, an endorsement of O'Toole's Conservatives makes sense for Quebec on a certain level, I think, in the sense that the Conservatives often favor more autonomy for the provinces and Quebec compared to the other Canadian parties. However, they're also often stingier in terms of the amount of aid they provide to the provinces and Quebec relative to what they request, I would point out, so there's also a price to going along with the Canadian Tories.
You know what doesn't come with such a price? Supporting Quebec sovereignty in a principled way by voting for the Bloc Quebecois. Fortunately (at least in my opinion it's fortunate) that appears to be exactly what many Quebecers are doing right now despite their popular premier's endorsement of the Canadian Conservatives, as that same report above highlights. It goes to show the limits of even Legault's degree of overwhelming popularity (some 80% of Quebecers approve of his job performance according to recent polling) and that many of his supporters actually occupy a political space to his left.
As to your comparison of Canada's Conservative Party to our Republican Party here in the U.S., let me just say as an American myself that that comparison is patently absurd. The current leader of the Canadian Conservatives, Erin O'Toole, has publicly declared himself pro-choice, a supporter of Bill C-16 (the sweeping gender identity bill that has resulted in the de-funding of Vancouver Rape Relief and Women's Shelter over their shelter's women-only policy, among other things...which, let's face it, is what Canadians actually mean these days by "LGBT rights" and the kind of legislation I'd rather not see imported here, personally), taxing carbon emissions, and a whole raft of other social policies that frankly I cannot even imagine someone analogous here, like a Republican presidential nominee or a the Chair of the Republican Party ever endorsing, ever. Frankly, even the Canadian Tories' of budgetary hawkishness is quite mild compared to what many Republicans in this country support. Some of these policies for their part are new; a slight, conciliatory leftward shift made under new leadership selected after their second electoral defeat in a row two years ago that effectively renders them basically just a lite version of the Liberal Party on almost every issue. There are Republicans like that in this country (such as Vermont Governor Phil Scott, Massachusetts Governor Charlie Baker, or Maryland Governor Larry Hogan, for example), but they're today only politically viable in the liberal-leaning American Northeast and ideologically represent less than 15% of Republican partisans overall. They're different from their Democratic counterparts mainly just in that they veto minimum wage increases and such (and may well get overriden at that). They even take Covid seriously and favor Western-style democracy over the emergent police states of Russia and Eastern Europe, just to be revolutionary. The Coalition Avenir Quebec seems very much like this as well in most respects in my observation.
No, the closest analogy to our Republican Party in Canada, and in this election, can be found squarely in the anti-immigrant, anti-abortion, pro-Covid People's Party of Canada, the very creation of which was obviously inspired by the election of Donald Trump to the American presidency in 2016 in the first place. Not exactly being a fan of our "GOP" here, I'm particularly unimpressed with the PPC there.