No, we don't. This is not an yes/no answer. This is the type of question that should be answered in terms of confidence intervals.
> right wing tweets actually got promoted more
In relation to what? What is a "right wing" tweet? What is a "left wing" tweet?
E.g, if the algorithm is focused on filtering out disparaging extreme messages, and it ends up filtering X amount of "non-extreme right wing content", 3X of "extreme right-wing content" and 5X of "extreme left-wing content", it satisfies the claim that "it promotes more right-wing content" while also silencing conservative voices.
This is not exclusive to Twitter, but here's a recent research papaer on the comparative advantage of "the right" in dissimination of information on social media.
