Except the US constitution does not include that language. The “a wall of separation between church and state” phrase most notably comes from an 1802 letter by Thomas Jefferson to the Danbury Baptist Association. Not a legally binding document by any means.

I imagine you’re thinking of the Establishment Clause of the Constitution which forbids the US government restricting the free exercise of religion.

I believe, iirc, the Supreme Court over several decades has affirmed and reaffirmed the overall position that the US government must remain secular and not favor a particular religion. Which is effectively what you’re getting at.