Is there an essential question about Geraldine Connolly's poem, "The Summer I was Sixteen" -- a question that helps students consider the poem's main meaning?

I would suggest something like this:
"How does the poet convey the vivid, subjective impressions of a 16-year-old, while also indicating that the narrator has evolved, and now sees these memories in a different light?"
Here's why.
Obviously, deciding if a question is "essential" depends on a certain amount of subjectivity. But this poem is clearly presented as the recollection of an older woman about her experiences and perceptions as an adolescent. It is just as clearly concerned with evoking vivid sensory impressions, and it makes us aware of two, sometimes conflicting perspectives: The teenager's and the adult narrator's.
So while readers may disagree about shades of meaning, I think most will acknowledge that the meaning of the poem concerns these two points:
(1) what it felt like to be a sixteen-year-old enjoying a carefree summer day, and
(2) what it feels like to revisit those feelings from a different perspective -- the perspective of an older, wiser person whose sense of self and the world has expanded or become more complex.
That's what gives the poem its distinctive emotional character: It isn't just a nostalgic collection of sensory memories. It's a poetic reflection on the distance between the current self and the past self -- on our ability to re-experience vivid memories of the past while also considering them from another, more mature perspective.
So if you want a question that asks a student to discuss these meanings, I think the question above is on the right track.
A student answering such a question will be forced to consider not only the imagery that evokes the teenager's experiences. The student will also need to address the evidence of conflict in the poem -- the conflict between the teenager's perceptions and the narrator's understanding.
It is essential, for instance, to notice that the past self "did not exist beyond the gaze of a boy," and that the teenager and her friends tossed a glance through the fence at "an improbable world." We can surmise that the narrator now feels differently about these things.
She knows she exists beyond the gaze of boy, and accepts, with apparent amusement, that her teenage self did not. The bigger world beyond the fence is no longer "improbable." She has had to venture beyond the fence, and learn first-hand what the world is like.
In light of these contradictory perspectives, and the vivid imagery of this poem, it may be helpful to read an interview that the poet gave in 2010 (see link below). In it, Connolly said:

I have a visual mind and imagination. I would have like to have been a painter. I think of an image as a word picture, an intense electric connection between the eyes of the writer and the mind of the reader.

So imagery is essential to her. But in this interview she also noted that she's  intrigued by images that are in some way self-contradictory or paradoxical, referring to examples from Emily Dickinson and other poets.
In particular, note what she says at the end of this quote about contradiction feeling honest or true (words I've printed in boldface):

Some of the other great image makers are Dickinson: “frost, a blonde assassin—”; T.S. Eliot’s singing mermaids who do not sing to him; Wallace Stevens’s “downward to darkness, on extended wings.” I love the way that image of pigeons’ wings descends and expands simultaneously. All of these images that come to mind include paradox. There’s something about contradiction that feels honest and true to me.