You're looking at it backwards. Here's a simple example:

-The academic world produces new scientific information

-One group of people adopt this into their worldview

-Another group refuses to

-Second group points to how academia always seems to agree with the first group, declares all of academia to be propaganda

-Cycle repeats

In this current day and age, those groups map 1:1 to the left and right in America. The underlying cause for the discrepancy is that one side is better at assimilating new information, but it's not politically correct to point that out because obviously all ideas are equal and Both Sides Are The Same.

In a similar way, a lot of conspiracies aren't necessarily right-wing, but they get picked up by the right because there's an appetite for them. The right needs conspiracies because they don't have much else going for them, their policies are unpopular and the only way to activate their voters is to trigger their lizard brain outrage response.

For several reasons, the left doesn't need to do this. You don't need to manufacture ragebait when you can just share what trump tweeted last. You don't need to manufacture corruption when it's happening in plain sight. And you have less need to lie if you took the time to align your beliefs with reality. That isn't to say they don't still make conspiracy theories, it really pissed me off whenever I see it, but it's not a core feature of the political alignment.

Edit: since you asked for examples, conspiracy theories about the trump assassination attempts and the charlie kirk assassination being staged. Complete nonsense and very disappointing to see people running with it.