Learn English – the name of this rhetorical device involving the use of One. Word. Sentences. For. Effect

There are several possible descriptive terms for this rhetorical device. The most appropriate seems to be:

chiasmus

a reversal in the order of words in two otherwise parallel phrases, as “flowers are lovely, love is flowerlike” (Coleridge). — chiastic, adj.

what is broken is made whole again,
what is soiled is again made clean.

The others are:

epanados

1. the repeating of a phrase or sentence in reverse order.

what is broken is made whole again,
what is soiled is again made clean.

anastrophe

a rhetorical device in which the usual word order of a phrase or sentence is reversed.

But what exactly is a rhetorical device? According to Wikipedia:

In rhetoric, a rhetorical device or resource of language is a technique that an author or speaker uses to convey to the listener or reader a meaning with the goal of persuading him or her towards considering a topic from a different perspective, using sentences designed to encourage or provoke a rational argument from an emotional display of a given perspective or action. Note that although rhetorical devices may be used to evoke an emotional response in the audience, this is not their primary purpose.

Emphasis mine

As a celebrated statesman of the 20th century, Dag Hammarskjöld demonstrated astute oratory and writing skills by choosing words, building phrases and designing sentences in a logical framework that appealed to the powerful pathos and ethos of his audience. He would have made a sufficient impact if he had simply applied the rhetorical device of metaphor:

Forgiveness is the answer to the child's dream of a miracle by which
what is broken is made whole again.

Regardless of the word order, he applied the literal terms broken and whole to the relational dynamic of forgiveness. He could have increased the impact of that statement by simply adding a second metaphor with the rhetorical devices of repetition and parallelism:

Forgiveness is the answer to the child's dream of a miracle by which
what is broken is made whole again,
what is soiled is made clean again.

His repetition device can be further classified into three separate repetition devices: Anaphora, Epistrophe, and Mesodiplosis. Apparently, he wished to multiply the impact of his statement with the specific emphasis of a fourth rhetorical device of chiasmus:

Forgiveness is the answer to the child's dream of a miracle by which
what is broken is made whole again,
what is soiled is again made clean.

Accomplished authors, like Dag Hammarskjöld, choose to employ the flexibility of English semantics and syntax to make an intentional logical and emotional impact on their audiences, who often enjoy the impact without ever recognizing the author's devices. We enjoy discovering and discussing their techniques with relish.

Preterition may fit. Here is the definition in Dupriez, Bernard Marie, and A. W. Halsall (translator). A Dictionary of Literary Devices : Gradus, A-Z. U of Toronto, 1991 (quote from p. 353.):

"A figure by which summary mention is made of a thing, in professing to omit it" (OED). See also Lanham, Lausberg, Littre, and Morier. Both Quinn (pp. 70-1) and Fontanier (p. 143) add that such a declaration of omission is in fact a way of emphasizing the allegedly omitted material.

In each of your examples is something quite similar - summary mention of a thing in professing that a speaker omitted it, in order to emphasize the allegedly omitted material. To use your first example:

1. Just then his disciples came back. They marveled that he was talking with a woman, but no one said, “What do you seek?” or, “Why are you talking with her?” (Gospel of John 4:27; ESV)

Stating the omitted questions has the effect of emphasizing them. No one may have said them, but it suggests that others in that situation would have asked, or that these questions were seen as reasonable if a wise man like Jesus talked with a woman. Similarly, the other two examples further qualify the response of the two men to the day and the response of the angry man.

The main oddness here is that examples of preterition are usually in first person rather than in third person. However, nothing in the definition forbids its application to third-person narration.

Possible synonyms include include paralipsis/paralepsis or occupatio, though note that at least one scholar has disputed that preterition should be called that (Kelly, H. A. “Occupatio as Negative Narration: A Mistake for ‘Occultatio/Praeteritio.’” Modern Philology, vol. 74, no. 3, 1977, pp. 311–315.):

Quite clearly, then, preterition [and not occupatio or occultatio] is the appropriate term for Chaucer's usual practice of negative narration [...] (p. 315)