What is the ending of the 2004 American movie Before Sunset? It is best to be more detailed.

My favorite chatty movie, no one...

After they met in the bookstore, they walked and talked to Celine’s house, and then they continued chatting. Celine said that she was writing songs, Jesse said he wanted to listen, so he sang to him, and then he played the song. Celine imitated a star (it seems to be a star, if I remember correctly) and spoke. The last sentence was baby, you are gonna be late for your plane (the original words are probably not This, in short, means you will miss the plane), cut the scene, Jesse is smiling at her on the sofa, no more...