You have 2 questions:
- Is it authentic? - Yes.
According to Metro investigating how images were released from Covenant documents
Nashville Mayor Freddie O'Connell said he and his administration were looking into the unauthorized release of three images from the Covenant school shooter's writings.
This comes after conservative talk show host Steven Crowder released some of the documents from The Covenant School shooter on Monday.
“I have directed Wally Dietz, Metro’s Law Director, to initiate an investigation into how these images could have been released," O'Connell said. "That investigation may involve local, state, and federal authorities."
The mayor does not question the authenticity of the images, only how they got leaked.
- Is it being suppressed? - Maybe.
According to Crowder himself on Twitter, yes.
Objectively, there's no way to tell for sure, but while stories are present on Facebook, a quick comparison of the ratio of Nashville vs Maryland shooter (who was more recent, right-wing and received wide mainstream coverage) posts right now on Twitter (which presumably does not suppress under Musk's ownership and this has blown up on) vs Facebook, suggests that FB may be shadow-banning/deprioritizing this story (or Twitter is just more right-wing now, so organically interacts with this more.)
EDIT: I just realized I misinterpreted the second part of the question.
Was this "suppressed" by the police? Unknown.
According to Nashville police withhold Covenant shooter's writings amid lawsuits seeking release, the manifesto was supposed to be released in April:
Calls for the release of the materials — which TBI Director David Rausch characterized more as "ramblings" rather than writings pointing to any clear motive — have been growing over the past few weeks, heightened by Gov. Bill Lee’s statement made on social media on April 27 declaring that the information would be “released to the public very soon,” as well as his calls for a special session to pass his proposed gun control legislation.
But then, next month that didn't happen because:
Metro wrote in a court filing Wednesday that "some parents from The Covenant School have informally indicated to the MNPD that they oppose the release of the shooter’s writings."
"The Metropolitan Department of Law has worked with the Metropolitan Nashville Police Department to review documents concerning the tragic shooting at The Covenant School," Dietz said in the statement. "Two parties have now filed litigation requesting voluminous documents. We are asking the Court to conduct a status and scheduling conference so that all interested parties may appear and raise any concerns. We believe family members of the victims should have the opportunity to present any concerns or objections to the Court at that time. We plan to file under seal the entire journal found in the shooter's car in the parking lot at The Covenant School together with our proposed redactions, under the Public Records Act, for the Court to review for release."
The allegation is that there are un-stated reasons (makes trans people look bad) in addition to the stated ones.