While sympathetic to your critique (and the AHA's stance), Trinity Lutheran Church v Comer fits well within past precedent of how the Constitutional separation of church and state operates here in the US.
It appears to me (IANAL) that the controlling precedents may include Everson v Board of Education which allows public funds to be used by students of religious based schools under certain restrictions and Lamb's Chapel v Union Moriches Union Free School District forbids excluding groups based solely that they are religious from applying for the same benefits and services that are available generally to all groups. And since this is restricted to just funding for the playground upgrade, it appears to me that it passes the Lemon test (disclaimer: I have not read Lemon v Kurtzman or other cases that explicitly invoke the Lemon test.)
Having skimmed the written opinion, though, I do have some qualms. There are some strange things there that make me suspicious that Roberts is trying to get ready to pare back the separation of church and state. Gorsuch and Thomas wrote concurring opinions that pretty much seems that they are ready to gut church/state separation pretty drastically (Thomas isn't a surprise here, and Gorsuch merely replaces Scalia in this regard.)
I am sympathetic to Sotomayer and Ginsburg's dissent, but (and you need to take into account my lack of formal legal training) I think I would disagree with their legal reasoning.
Sorry for the verbage - especially if it's off-topic. It's one thing to express an opinion on what one would think the perfect situation is, but many of my fellow Americans confuse their pesonal opinions about what they would prefer with what the Constitution actually says and allows, an understanding of which requires a not-particularly deep knowledge of past precedents and how Constitutional law operates in this country.
As I've had to admit before, we are stuck with the Constitution that we actually have, not the one I would prefer.
Freedom is merely privilege extended, unless enjoyed by one and all. — Billy Bragg