I have mixed opinions about the second Violet Evergarden movie. I feel it would have been better, and easier to follow, had it all been set the the "present" rather than in the future with Violet's story told as history.
Some series, movies and books often leave me with the feeling that I want to know more of the lives of the characters. I think this happens when the author has crafted their story so well that you come to believe the characters are real people and they almost become part of your life. This can lead to the series or book having sequels which sometimes work but can become a franchise which extends the story beyond it's natural length and risks devaluing the original work.
As for that feeling you get once the credit roll ends or the last page is turned I think all you can do is treasure that feeling and mark the series, movie or book down for a rewatch or reread later on.