The New York Times has a lengthy article about Professor William English, who has written articles and briefs about gun ownership. Buried towards the bottom of the article is some new reporting on the deliberations in Bruen:
The draft opinion that Justice Clarence Thomas circulated to his colleagues in February 2022 was sweeping, with the potential to outlaw many common gun-control measures. The majority was slow to sign on. Chief Justice John Roberts and Justice Kavanaugh requested modifications, according to people familiar with the deliberations, who requested anonymity because that process is intended to be secret.
By May, Justice Thomas still had not mustered the five votes needed. Mass shootings that month in Buffalo and Uvalde galvanized public attention anew on gun violence. It was not until June that his opinion prevailed, when Justice Kavanaugh signed on but wrote his own more moderate concurrence, joined by the chief.
The authors, Mike McIntire and Jodi Kantor, do not provide any more details on their sourcing. I've heard that Kantor, whom I blogged about recently, spent some time researching the OT 2021 Term, and the Dobbs leak in particular, so I wouldn't be surprised if she gained some information about Bruen. Like with Joan Biskupic's reporting, I will remain skeptical, though presume it is true for purposes of the analysis.