I really think Sasuke sent his messenger hawk to Sakura on purpose because he wanted her to give his letter to Naruto with him, like how couples attend a ceremony together and give their congratulations together. He knows Sakura will get lonely because he wasn’t around so it’s his way of making it up to her.
He could’ve just sent it to the Hokage Kakashi but he chose her instead. It shows that Sasuke thought about Sakura’s feelings even during his travels.
It took me a while to realize this but when I did I was like ASFDSHFJKSUKDSNVKLABVSAGVSKABDHB *FANGIRL SCREAM*