I read this poem as largely playful in nature. Starting with the title, “This is just to say” already gives the idea that whatever occurs next, is not to be taken seriously. From the title alone, the speaker is trying to play off their transgression.
I interpret this poem as taking place in a domestic setting, and “the plums/that were in/the icebox” is in a shared, common area. As such, the speaker is at the very least acquainted with the person they are apologizing to, and possibly living with them. This feeling of familiarity is also evident in the second stanza. The speaker is close enough with this person to know their intentions and habits, that they “were probably/saving [the plums]/for breakfast.”
The enjambments add some humour to the poem. It creates a comical image, as if the speaker is speaking slowly and haltingly, like they are delivering news that require the addressee to seriously process what they are saying, or giving space for the addressee to brace themselves for the next line.
In the second stanza the speaker, again, is trying to brush off their theft. They admit guilt sheepishly, as if they don’t mean it, breaking up this short clause with the enjambments. The line “you were probably” stands alone, like an aside that could have been surrounded by em dashes or commas. It is an incredibly indirect line. The speaker doesn’t want to acknowledge that they really knew the addressee’s intentions with the plums. They add ambiguity to lessen the impact of their theft. And because the line stands alone, the emphasis is on that ambiguity.
The enjambments in the last stanza, gives it a mocking tone, which, can still be quite playful. The speaker describes how great eating the plums were and rubs it in with each line. “They were delicious/so sweet/and so cold.” One can imagine a pause after each line despite the enjambment, adding their own mental end stops. The speaker just emphasizes how good it was to eat these stolen plums, slowly, and tauntingly. It is the sort of play that you can only do with someone who is close to you, and who you may even love.