I basically agree with your analysis all the way through except for this. You are just stating how the left wants to use "tools to vitalize the population and lead to a sort of spiritual awakening of the nation"!
In both cases, you have strong foundational beliefs that are not really open to question but usually have strong moral rationalizations (though the specific moral appeal is different). In both cases, truth is not a thing to be discovered but an idea that people have that should be manipulated to achieve your ends.
So I don't view the relativistic left as particularly different from the propagandistic-authoritarian right. The latter is a greater danger right now and has gotten deeper in along the post-truth path, but handing power from one post-truth side to the other simply shifts the locus of danger without diminishing it.
The biggest problem I see with the left is that in failing to insist that, "no, really, honestly, always, we base our ideas in reality," it gives away the most devastating weapon to use against the propagandistic-authoritarian right. Because all the left has, then, is different propaganda.
(I do not have good resources on Foucault, alas. I find pretty much all the postmodernists infuriating to read; the detailed summaries I've found aren't much better. Also, I name-dropped Foucault, but I don't blame him specifically but rather that whole philosophical lineage. I consider Nietzsche a pre-postmoderist, so I do in fact attribute Mussolini's ideas in significant degree to the same intellectual quasi-philosophical lineage. Not Machiavelli, though. It's not like it's a new idea that you can gain power or achieve your ends by BSing people. What was new was the vigorous intellectual attack against the typical way to get out of it, which is to call the BS BS.)