I think it'd be 6-3 the other way. The removal of religion from schools has been one the biggest points of contention on the right-wing. It's probably second only to their attack on abortion rights. I think this is far more insidious though, as the plain text of the Constitution is clear as to religion.
The Establishment Clause is one of the only clauses in the Bill of Rights whose plain text actually goes a bit further than what even most social liberals want, or at least want to make a federal case out of right now. Special cases like cross-shaped monuments that are now of historical value themselves aside, a rigorous Establishment Clause analysis of things like "In God We Trust" and the expressly theistic version of the Pledge of Allegiance probably junks those things even though doing so is not currently very high on the socially liberal/SECULAR wish list.
Yes, this is one case where textualism clearly favors the left. A public school compelling students to participate in a religious ceremony of any kind is no-go land taking the Establishment Clause literally (voluntary meetings of religious student groups outside of class are probably fine, though).
I do think Engel would still win. You would almost surely have Gorsuch writing that compelling students to participate in a prayer to a God they don't believe in violates their religious freedom, so the absolute best case for the school district is 5/4 in their favor if it follows the traditional divide. But it would be very hard to get all 3 of Roberts/Kav/Barrett. Roberts might vote for the school district on stare decisis/minimalism grounds, but Kav and Barrett would likely find the Gorsuch religious freedom argument very persuasive. Also, remember that many of the school prayers in that era were explicitly Protestant and that 5 of the 6 SCOTUS conservatives are Catholic.
The school district's best bet would be to argue that if they lose on prayer, it would lead to certain "woke" material or presentations in a school being unconstitutional and make a play for Sotomayor and Kagan (who has a stare decisis/minimalism streak like Roberts). If the school district wins, they probably win with Roberts, Sotomayor, Kagan, Thomas, and Alito, as strange as that sounds.
