The contention you are trying to challenge is that Twitter amplified right wing posts more than left wing posts in the pre-Musk days.
Your link fails to support you. It is mostly just examples of alleged Twitter censorship, mostly of right wing-ish stuff. This has a couple of problems.
First, the claim was about what Twitter amplified, not what it censored. It is quite possible to both amplify a given type of post more and censor that type of post more. It is possible that censorship might inversely correlate with amplification so that one can be used as an inverse proxy for the other, but that would require research because it is also possible they correlate rather than inverse correlate. Something amplified draws more readers, which could increase the likelihood that someone will notice any violations of the rules and report it.
Second, even if we make the assumption of an inverse correlation between censorship and amplification to see how left and right amplification compares we would need to know how they picked which incidents to write stories about.
Reclaim the Net does not provide any information on who funds it or who runs it, it is asking for donations but doesn't say what the donations are used for. The names listed on it don't show up in search except at RTN or on sites that are reprinting RTN stories. There is just not enough information available as far as I could find to tell what biases they have when selecting stories.
The commenter you asked for proof cites a published paper in a peer reviewed open access journal that gives a detailed explanation of how it reached its conclusions. Its authors include several people who worked at Twitter and had access to its internal data.