I agree with @user121863 that the example you give is certainly a type of repetition, and I would cite the same source (literarydevices.com).
I would just go a step farther to be a bit more specific. Repetition is a term that covers a full set of different literary devices. Most of these describe using repetition within a particular sentence, paragraph, or verse.
I think that refrain, which is a particular kind of repetition, may suit your purpose.
The term refrain is most commonly used for poetry or songs, when a particular line or phrase is repeated regularly, at the end of multiple stanzas or verses, or between them (Cambridge).
But it can also be used in prose. From litcharts.com: "The term refrain has come to have a meaning that is a bit different, and less specific, in the context of speeches or prose writing. In such writing, a refrain refers simply to any phrase or sentence that is regularly repeated."
So for the phenomenon you're describing, I'd suggest refrain, which is a type of repetition.