NULL doesn't really mean unknown; it means that instead of having a pointer to a result-set, you have no such pointer.
But in the semantics of answering questions, ala Prolog, "the absence of a result set" means that you don't know something, since those "results" are the answers to a question.
An alternative way to think of NULL is that it's a short-circuiting of what would otherwise be the database blocking on a promise for data to resolve, that never resolves—waiting for its deductive algorithm to get the data necessary to definitively answer the question.
> have MISSING and UNKNOWN as two different concepts
You already do. Just have a boolean column "foo_present" (or an enum column "foo_type", where one type means "intentionally absent") beside your nullable whatever-typed column "foo". In this case, a foo_present=TRUE together with foo=NULL means you're missing the foo value that you really expected to be there—it's a semantically-present, in-practice-unknown value (which probably indicates that e.g. the enrichment step hasn't gotten around to filling it out yet.) Meanwhile, if foo_present=FALSE, the value of foo itself doesn't matter (though it probably should be NULL) since you won't be looking at it in the first place; whatever value it has in practice, it's not meant to have a value semantically. It's pretty easy to construct queries around this paradigm.
Or, if you're using a SQL RDBMS that supports custom types, you can just declare a sum type, e.g. Pet = Present pet_id | Nothing.
Or, if you're using an SQL RDBMS that supports array product-types (e.g. "int[]"), you could just use an array-typed column with a CHECK constraint on it limiting it to have either 0 or 1 value. Then a value can be [], [foo], or NULL.
All of these allow you to see when the information of absence has been explicitly entered, separately from the query-response of unknown-ness which can come from a variety of places (such as e.g. joining several tables for sub-types of something together, where the columns that don't exist for a given sub-type will appear NULL.)