It might introduce new mechanics. For example, if the new story involves a new type of magic or power, there could be gameplay elements related to that, like new skills to learn.
They add depth. For example, when you play as Amber and know her story, you might play with more care and try to make her feel more important. It makes you more invested in the character.
If 'childe chopsticks fanfic' is a relatively unknown piece, it might be difficult to analyze in great detail without more context. However, generally speaking, if Childe is a character from a game or a story, the fanfic might explore different aspects of his personality through the use of chopsticks as a symbolic or plot - driving element. For example, the chopsticks could be used in a cultural context, like in a traditional meal setting that reveals something about Childe's background or his relationship with other characters.
Childe 3: Ambitious Hero is the name of a novel. There is no official announcement of its follow-up story. However, according to the author's writing habits, there would usually be sequels or side stories, so he could look forward to whether there would be any relevant information leaked.
As of now, the Genshin manga is not finished. The story is still evolving and there's more to come for fans to enjoy. The creators are taking their time to develop a rich and engaging narrative.
There's no definite answer yet. It might continue if there's enough demand and the creative team has more story to tell. But it could also stop if they feel they've completed the story arc.