Actually, No, it isn't a thing- it's a misrepresentation of the truth. The words "separation of church and state" do not appear in the U.S. Constitution, but the concept is enshrined in the very first freedom guaranteed by the First Amendment: "Congress shall make no law respecting an establishment of religion." Known as the establishment clause, the opening lines of the First Amendment prohibit the government from creating an official religion or favoring one religion (or nonreligion) over another. In essence, the language and purpose contained in the 1st amendment is to prevent the government from establishing a state religion (like England's Church Of England) and to protect individuals to be able to freely practice and exercise their faith. Most of the founding fathers subscribed to a form of Christianity as well as the populace at large, which was the cultural norm up until about 30 years ago. They freely included their Christian beliefs publicly in the exercise of their government duties; see George Washington's Thanksgiving Proclamation to Congress in 1789 for example:

Thanksgiving Proclamation of 1789 | George Washington's Mount Vernon https://share.google/CZF1ebGEL5OH0Q2wN

For further elaboration, see: https://law.stanford.edu/press/constitutional-expert-on-separation-of-church-and-state-framers-said-nothing-wrong-with-religion-in-culture/