I'm working with a set of particularly American definitions. Our Democratic Party encompasses everything from left to center-right, so it's a very mixed bag.

Your definition of the left doesn't really apply here in Canada's basement. We don't even have a functioning far left, they're just a noisy faction that rarely gets their way - but you'd never know that to listen to the GOP.

Democrats are far more fiscally responsible than Republicans - deficits go down when a "Socialist" is president and up when a "deficit hawk" is. It's a little weird.

The whole "woke" thing you're describing is primarily a right-wing fiction. The word doesn't have any real meaning anymore. The right gets hold of certain words and phrases, strips them of meaning, then redefines them. Critical race theory is the best example:

“We have successfully frozen their brand—'critical race theory’—into the public conversation and are steadily driving up negative perceptions. We will eventually turn it toxic, as we put all of the various cultural insanities under that brand category. The goal is to have the public read something crazy in the newspaper and immediately think 'critical race theory.’ We have decodified the term and will recodify it to annex the entire range of cultural constructions that are unpopular with Americans.”

https://www.washingtonpost.com/education/2021/06/19/critical-race-theory-rufo-republicans/

There are "I get offended easily and want to cancel people" crazies on the left, but the right is the undisputed champ at both. For an easy example, every conservative will rant on and on about "cancel culture and taking books off the shelves." But every year for my whole life, most of the challenges to library books are by conservatives. That sort of thing.

Maybe as a Canadian, you don't know what it's like to have one of only two political parties dedicated to the project of a fundamentalist Christian theocracy...

They soil themselves every time anyone makes fun of their religion, they're passing laws that allow parents to sue teachers who upset their children, and on and on and on. Ain't no snowflake like a right-wing snowflake. But they are really good at pitching a narrative, and that's what they've done.