Consider the following two sentences:
1. The fact that he is a brilliant student is not unknown to no one.
2. I know that he is a brilliant student,
Here He is a brilliant student is a Declarative Content clause, which by itself is independent, but when it is part of a larger constituents [part of a Noun Phrase (NP) in #1 and part of a matrix clause in #2], it becomes subordinate clause. And that that just introduces the subordinate clause. The sole purpose of that is just that - to introduce a subordinate content clause. We classify it as a Subordinator.
In #1 the subordinate clause functions as a Complement of the Noun - fact, and in #2 as an internal complement of the Verb - know.
Now consider the following sentences -
3. The book which I borrowed from Noelle is excellent.
4. The book that I borrowed __ from Noelle is excellent.
Now which I borrowed from Noelle and that I borrowed from Noelle are also a subordinate clause but it is different from the ones we saw in #1 and #2. Here they are Relative Clause. It has completely different structure. Even unlike the first set of sentences, it here functions as a modifier in NP structure. It modifies the Nominal - book and the whole Noun Phrase is the book which/that I borrowed from Noelle. Structurally it is different in that it has an antecedent - here book, and which is referred to by the presence of relative pronoun which in its Prenuclear Position in case of #3 and is referred to by the presence of a gap in the normal expected position in case of #4. In #4 though that I borrowed from Noelle is a relative clause, the that here is not a relative pronoun (though Traditional grammar call it that). This that here is also a subordinator.
So the important takeaway is that that can introduce both a content clause and a relative clause, but it is the presence of gap and antecedent that tells which one is relative clause.
Again note here, that is always a subordinator irrespective of whether the clause introduced is a content clause or a relative clause. In traditional grammar that in #1 and #2 is a conjunction and in #4 is a relative pronoun.
Back to you sentence:
There are so many hot springs that visitors can experience the same types of bath as the ancient Romans enjoyed.
Here in the subordinate clause there is no gap like #4 above or any antecedent like #3 and #4 above. It is not a relative clause; it is a declarative content clause.
In your sentence that is a subordinator. Or if I take the terminology of traditional grammar it is a Conjunction and not a relative pronoun.