Here's a link to the oral argument transcript.
Page numbers are Adobe numbers for easier searching.
See pages 4-5.
chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.supremecourt.gov/oral_arguments/argument_transcripts/2021/21-418_j4ek.pdf
Breyer questions the facts in the lower court records on pages 19-23. Nothing contradicts the facts stated in the opening.
There's a discussion about praying at practices on page 33. Kennedy apparently discontinued that.
Respondent's opening statement is on pages 57-58. There's a slight difference in how the facts are stated.
Even with the differences stated by the lawyers, nobody was required to join the prayer. Kennedy did go out of his way to "invite" others, including the press and opposing teams.
The issue of possible coercion was discussed throughout the entire session.