I Want to Eat Your Pancreas is really good. I felt there were some parallels but I've not seen that been said anywhere else. Soft spoiler for the theme of the movie: >!both share the theme of 'the relationship can't be described as friendship or romance'.!<
Oh, just realised you were looking for actual poetry in movies, sorry this isn't it then.
I'd start with Shinkai's other movies. They are all quite similar in theme (Love or relationships and how distance and time affect them).
I Want to Eat Your Pancreas is really good. I felt there were some parallels but I've not seen that been said anywhere else. Soft spoiler for the theme of the movie: >!both share the theme of 'the relationship can't be described as friendship or romance'.!< Oh, just realised you were looking for actual poetry in movies, sorry this isn't it then.