I've an older post where I thought about this once.
More of the here and now though,
I think that the separation of Church and State can also be understood informally.
In the way that unspoken but assumed rules are.
Of course people 'vary in how much they think Church and State should be separated, 'plenty of lawmakers heavily involve Church and State together.
https://www.debateart.com/forum/topics/11231-ten-commandments-in-classrooms
"Separation of church and state" is a metaphor paraphrased from Thomas Jefferson and used by others in discussions of the Establishment Clause and Free Exercise Clause of the First Amendment to the United States Constitution, which reads: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof".
https://en.wikipedia.org/wiki/Separation_of_church_and_state_in_the_United_States#:~:text="Separation%20of%20church%20and%20state"%20is%20a%20metaphor%20paraphrased%20from,an%20establishment%20of%20religion%2C%20or
Well, state government isn't 'Congress.
"In keeping with the lack of an established state religion in the United States, unlike in many European nations at the time, Article Six of the United States Constitution specifies that "no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States",
https://en.wikipedia.org/wiki/Separation_of_church_and_state_in_the_United_States#:~:text="Separation%20of%20church%20and%20state"%20is%20a%20metaphor%20paraphrased%20from,an%20establishment%20of%20religion%2C%20or
In 1961, the Supreme Court ruled in Torcaso v. Watkins that a person could not be denied the office of notary public for not being a believer because it "unconstitutionally invades his freedom of belief and religion guaranteed by the First Amendment and protected by the Fourteenth Amendment from infringement by the States."
https://www.statesman.com/story/news/politics/politifact/2021/11/10/7-states-ban-atheists-office-but-bans-unenforceable/6352254001/
But 1961 is a long way from 1776,
And yet seven of the states mentioned in the post have language in their constitutions explicitly prohibiting atheists from holding office. Mississippiβs constitution, for example, states that "No person who denies the existence of a Supreme Being shall hold any office in this state." In Pennsylvania, the eighth state noted in the post, the rule is not as clear cut.
https://www.statesman.com/story/news/politics/politifact/2021/11/10/7-states-ban-atheists-office-but-bans-unenforceable/6352254001/
Thomas Jefferson was not the 'sole definer of what people wanted of their government, or considered the law to be.
"In contrast to this emphasis on separation, the Supreme Court in Zorach v. Clauson (1952) upheld accommodationism, holding that the nation's "institutions presuppose a Supreme Being" and governmental recognition of God does not constitute the establishment of a state church the Constitution's authors intended to prohibit.[3][4]"
https://en.wikipedia.org/wiki/Separation_of_church_and_state_in_the_United_States#:~:text="Separation%20of%20church%20and%20state"%20is%20a%20metaphor%20paraphrased%20from,an%20establishment%20of%20religion%2C%20or
There are many other examples on Wikipedia,
But I'm just skimming,
At a skim though, it 'looks to me that a state 'can according to the Constitution, have the 10 Amendments in a school,
Or the Satanist 10 Commandments, if they had enough public and government official support.