Formalist theory focuses on a work's or a poem's literariness; what makes it different from everyday speech. Formalists want to distinguish literature/poetry from everyday language. Formalists do not see literature as an exact reflection of reality, but an artistic interpretation of reality. Since formalists focus so closely on text and form, they attempt to ignore or put aside cultural and historical implications. This method has its proponents and opponents. Opponents claim you cannot separate art from history, but most do not dismiss formalism as a valid literary practice; they just think it should be complemented with cultural, historical, feminist, etc. interpretations.
A formalist analysis would look at the line breaks, the grammar, the word choices and the themes as the poem exists as autonomous; sort of outside history. Generally, the poem is about the young girl inside the poet who refuses to die; so it is about keeping a young perspective even into old age despite. Formalism does focus on themes but moreso on the actual literariness of poems. So, what about the poem makes it a poem? What makes this poetry different from everyday speech? What makes it an unfamiliar way to speak? One thing is the pun with ‘thyme’ where the narrator will blossom into thyme meaning something new (blossoming into; second coming) and blossoming into ‘time’ as growing into the world of linear time.
The comparison between the narrator and the tree, as well as the woods with other people, is an example of personification or anthropomorphism. It shows a comparison/analogy between humanity and nature.
‘Green’ can mean natural, young but also naïve, or new. A formalist analysis would look at literariness and that means finding the different possible meanings; as authorial intent or reader interpretation. Puns, metaphors, synecdoche, metonymy are all elements to be aware of with formalist analysis.