To be clear, he wasn't "praying on the field". He was leading the whole team in prayer as part of the school event, at the 50 yard line, with the audience watching, inviting others to participate, apparently creating an atmosphere of pressure to participate, etc.. He was using his role as a coach and as faculty of the school to formally endorse and encourage his particular religion as part of the identity of the team.
And the stupid fucks at the SCOTUS thought this was not an establishment violation based on lies. Kavanaugh literally repeatedly lied in his opinion on it, claiming repeatedly that it was a private prayer instead of a giant, intentional public spectacle.
Anyone who looks at the photos of clips of the prayer will have ZERO illusion that this was a small private prayer on the field. It was a megachurch-inspired moment.