Yes. For that reason, Congress was prohibited from promoting a particular sect, but States were not prohibited.
The states had certain things they were not permitted to do. Those were articulated in Article One, Section Ten. Establishing a State religion was not prohibited.
Oh yes. But there is perhaps some confusion here over the term “state.” I’ve been talking just about the First Amendment and the U.S. Congress being prohibited from establishing a religion, which would be the “state religion.” And that was not just the invention of Jefferson, but it was a pragmatic decision since most of the public wouldn’t have accepted any one sect being established as the national or state religion before all the others.