This "aura" you speak of is a fabrication, and the product of right-wing narrative, which has been clearly effective at generating this impression.
No. They have it, because they embraced it. Even if it was just lip service in some cases.
Democrats were for: Defunding police, transgender insanity(or "rights" as the left would frame it), illegal immigration, "restorative justice"(letting criminals of a certain race get away with bad behavior), DEI, green energy pie in the sky nonsense, etc, etc. There isn't a hard left stance they didn't promote, except for maybe standing up for Palestine. Hence, why it was so easy for the right to frame them as such. If it quacks like a duck...
The major political campaigns by Obama, Biden, Harris had very, very little to do immigration and "chicks with dicks," or DEI.
I'd say that only Obama at least appeared genuine. Biden ran as moderate, but on Day 1 he cancelled pipeline production(oil bad!) and protected men being allowed to compete with women in women's sports(trans insanity). Kamala was just desperate and phony, and tried to convince people that she changed every one of her hard left stances stances in four years. Sure, you can claim that she ran a more moderate
campaign, but nobody bought it for obvious reasons.
That is, the party ran on a traditional welfare state agenda and moralism against oligarchic privilege, but it is a narrative that has ran its course and lost its persuasiveness.
Probably had something to do with them bragging about how many billionaires they had on their side. Then they lost, and all of a sudden didn't like their influence in politics. Hypocrisy is a big issue for them. Naked and profound hypocrisy that is(they're all sneaky bastards).
Clearly, most of them know that going 'officially woke' would be suicide, which is why they have never done that and have stayed within their usual rhetoric. But that is precisely what got them into trouble, not being able to change generate a rhetoric that is appealing massively and capable of luring back the working class, while making the right appear nauseating. The right, in turn, was very savvy and reinventing itself and turning from the crusty old moralist conservatism to a techo-liberatarian circus with entertainment and unhinged populist vulgarity, nevermind traditional values or morals.
I don't think we're too far off of each other, but I would argue that they did change their rhetoric(over years, not just on the campaign trail) to resemble a far left mantra. I agree that their main problem is authenticity, no matter how you slice it. They're trying to please everyone, and pleasing nobody.
I'm not sure who ever claims that "if the left embraced wokeness" it would do them any favors. If anyone does that's a really fringe and stupid position. There are a few people in congress that are of that stripe, but they are very, very few and far between.
There are plenty of "they didn't go progressive enough" folks out there.
The democratic party needs something besides what they are
Can't disagree there. What that actually is, I don't know, because they've kind of managed to burn both bridges. As a start, they need to get rid of the out of touch dinosaurs of the party, like Schumer and Pelosi, and realize that it's 2025, and Barrack Obama's influence over the party is not what it once was, and quit trotting him out there like a God.
You are confusing the perception of the party with what the party itself is.
The perception matters. It's not some right wing trick, that they're being thought of as far left nutcases. They did that all themselves. How they shed that association is anybody's guess, but they need to do it and quick, if they want to have any sort of chance continuing as viable party.
That all said, I'd say the media and the activists/pundits are their biggest problem. They can only say so much, but when you have outlets like MSNBC, CNN, the entirety of Late Night TV, etc, carrying water for them no matter what, they not only appear to be out of touch with the common person, but also appear to be the "Establishment" that people naturally fight against. No amount of FOX News is gonna shake the fact that they have most media organizations in their pocket spreading their propaganda. Hollywood in general is a big one.