I think you're giving a lot more benefit of the doubt to the Liberals (and US Democrats) than you should.
You're assuming they have wildly different aims. But I don't think history has borne that out. If you want to know why they're so tepid and inept in their opposition to the right and far right, it's because there's not enough of a substantial difference in fundamental direction and policy. (And liberals are on the whole conceptually unable to mobilize in a populist way because they distrust mass politics.)
Yes, on the cultural issues front there's substantial disagreement. Though less so in Canada where there's more of a socially liberal consensus.
But on the economic and political side of things, it's not clear to me that there's a strong ideological dividing line here.
Both are roughly in favour of the same neo-liberal economics. Private sector == good, low corporate taxes == good. Essentially supply side conformity.
But both are responsive to different bases.
The Liberals in Canada cannot move against social programs at this time, or cut social spending broadly -- but they absolutely have done so in the past. The Chretien Liberals enacted the most brutal austerity initiative in Canadian history, and in fact one of the most drastic in the entire G7.
At this point, the Liberals broadly support a kind of neo-Keynesian aggressive social spending. But I'd argue that this is not based on fundamental principles, but based on their need to acquire votes and to squeeze out the NDP. With inflation and various budget indicators being what they are, I am pretty sure the Liberals are prone to leaning back into an austerity direction ... if the NDP vote were to collapse completely, like it did in 1993 (down to 9 seats its worst performance ever), you can pretty much bet the LPC would be back to massive budget cuts. And I think Singh is taking the NDP in that direction, so.
I think you'll have a hard time seeing a strong economic policy differentiation between Harper's Conservatives and Trudeau's Liberals. (Or McGuinty/Wynne and Ford) Both responded with intensive social "stimulus" spending in economic crisis (2008 & 2020 respectively). Both used debt as a tool in a massive way. Neither side showed serious fiscal restraint. Both sides have kept a massively low corporate tax rate (one of the lowest in the western world and drastically lower than the "right wing" USA) Both favoured policies that pumped up the real estate market. Both had aggressive immigration and temporary foreign worker programs. etc etc.
... And both directed their spending at their respective voting bases in a way that verged on corruption (Harper threw money at Alberta in a huge way, Trudeau more in central Canada).
The basic fundamental difference between the two at this point boils down to which sector of Canadian capitalism they represent. The Conservatives are 100% aligned on the energy sector and its demands, and the ideological banners erected in its name in Alberta (along with all the climate change pseudo-denial/defeatism that goes with that). The Liberals represent different interests, some regional to QC, some of it sector-based (real estate & manufacturing). None of it altruistic, or principled, and none of it truly pan-Canadian.
And so here we are.