This claim is stating that media and FBI worked to censor and control a narrative. The narrative is not specified but we will be looking into particularly if FBI and media have worked to control posts. Based on the source Matthew Colin Taibbi was cited as the person who made statements that support this claim. He is an American author, journalist, and podcaster so fairly credible.
"We found one incredible e-mail from former FBI general counsel Jim Baker, reporter Michael Shellenberger found this, and it's essentially celebrating that the FBI had paid $3.4 million for, quote-unquote, 'processing requests.'"
According to multiple sources the FBI paid $3.4 million but as stated they did not claim this was becuase of censoring. Taibbi goes on to make opinion based conclusion including that this money could be paid because of censorship just as I could do so.
"So, in other words, all those requests that were coming through to Twitter, and we see all the e-mail traffic talking about what a burden it was for the company to process all of these requests, that's what the money was for. For them to look at all these requests for content moderation and censorship that were coming from all these different agencies."
There has been some consideration that there will be content moderation in terms of war and crimes. According to the NY Times there will be new rules that are not looking solely to delete content and adding fact checking labels.
https://www.nytimes.com/2022/05/19/business/twitter-content-moderation.html
In conclusion, I believe this claim is misleading because although one can assume, there are no hard facts that show the FBI and media have worked together to censor media.