It doesn't seem like you're familiar with how mathematical research is done. Taking 6 weeks between a major breakthrough on a huge proof, and making your proof public, is not unusual.
It takes a lot of time to finish a proof and figure out the best way to present it. I would personally be surprised if Buckmaster had not gotten it mostly cracked before June 29th.
The timeline here does not support your argument. Quoting from Buckmaster's statement:
Specifically: "For most of the past year progress was slow ... until about a month ago, when we had real progress: on August 15th"And you avoided addressing the critical issue: they weren't even solving the same problem. Buckmaster solved a simplified and easier version of Navier-Stokes. OpenAI solved a harder version eligible for the Millennium prize. Buckmaster did not.