Traditionally, linguists do not consider these forms to be a single constituent in English. Rather, it is thought that the entire that-clause is a subordinate clause embedded in another clause, called the matrix clause, as an argument of the matrix clause. For instance, if we have the sentence It is not the case that the sun rises from the west, then that the sun rises from the west is a complement clause of not the case, which would be called a 'complement-taking predicate' in Noonan's terminology. A classical treatment of these clauses is Noonan (1985/2007).
However, Thompson (2002) presents an alternative view that is more in line with what you have in mind. She argues against the traditional analysis, and calls these epistemic/evidential/evaluative fragments. Under her analysis, all three of your expressions would be known as epistemic fragments. It is nice that and It sucks that would be examples of evaluative fragments, and [subject] heard that and It's said that would be examples of evidential fragments.
Noonan, Michael. 2007. Complementation. In Timothy Shopen (ed.), Complex Constructions (Language Typology and Syntactic Description), vol. 2, 52–160. Cambridge: Cambridge University Press.
Thompson, Sandra A. 2002. “Object complements” and conversation: towards a realistic account. Studies in Language 26(1). 125–163.