Venti is my favorite character in Genshin Impact, and I think part of the reason I like him so much is that his intended character flaws and Genshin's unintended writing flaws synchronize quite well together.
My biggest issue with the way Genshin writes characters is that they are almost always static characters. With a tiny handful of exceptions, mostly within the main story, Genshin isn't interested in advancing character's arcs or showing them changing. Once we know their circumstances we know generally how they are, and parts of their story which seem to be hooks to further plot and development tend to fizzle out.
Normally this is something that stops me from really liking a lot of the Genshin characters, even if I think they're interesting; it frustrates me when the game seems to set things up and then refuses to follow through. But Venti, to me, is the exception, because a huge part of his central issue, in-universe, is that he is stagnant - that he has refused to move forward for 2600 years.
Venti's personal quest, "Should You Be Trapped in a Windless Land," is fairly up front about this. It involves the NPC Stanley, whose guilt over his friend's death decades ago has left him unable to move forward, clinging to the past. Venti spends most of the quest prodding and pushing at him, forcing him out of this mindset. But it is fairly clear that he does this in part because he sees himself in Stanley, that their situations are direct parallels, that Venti is in exactly the same place that Stanley was. When Venti says that he wants to see how Stanley will act when being forced to live in the present, it is in part because that is something he has never been able to do.
And so the story ends on a bittersweet note and an open ending. It's implied that Venti is going to be watching Stanley's progress closely; he can almost be seen as something like a test case. But what this will result in is deliberately obscured. If the player tracks down Stanley in the overworld after the fact, we learn that ever since the quest - which he has written off as a drunken dream - he feels happier and more fulfilled; he has resolved to himself that he does not have to choose between remembering his friend and living life, and has resolved himself to do both. So for Stanley's part, at least, things are going well. But as for Venti, things are less clear.
After all, he never actually says that he will change anything about his own situation, no matter how the Stanley situation resolves. Sure, he says he'll be watching, and that he's curious about how things will go. But to be honest, I always read this partly as wistful - that he wishes that he, too, could change, but that he feels that it is impossible for him.
He was the one who set this plan in motion - he knew exactly what Stanley's problems were, and how to go about helping him. Despite his carefree and lackadaisical attitude he is both experienced and self-aware; unlike Stanley, who denies that anything is wrong and cannot see the ways in which he is hurting himself, Venti clearly understands that the way he is grieving has long crossed into the realm of self-harm, and has known for a long time. But his friend died 2600 years ago, and hurting himself in his memory has become almost more familiar to Venti than the bard was. It is a key part of his self-conception, in a way that he cannot bring himself to shake. And he has multiple human lifespans to come to terms with this; to become comfortable as he is.
Which means, uniquely among the characters, that Venti's arc doesn't really have a burning need for a conclusion. There's no ticking time bomb that needs to be addressed. He doesn't have big interpersonal problems that constantly beg to be untangled like Kaeya and Diluc, or big future plot hooks like how Albedo worries that he will become a threat to everybody he cares about. He isn't in a situation where if the game ended today, players would feel like he never got his story told. Because in a way, already have an arc for him. It's a deeply sad one, is all; one where he acknowledges that he's been stuck for a long time, and will remain that way.
Certainly it is possible to continue his arc. It's very easy to imagine a future writer giving him a happy ending with a storyline where he tries to find hope in the future again, or even a tragedy that makes it explicit that he will probably be reliving the past forever. But it isn't strictly necessary. This I think is a big contributor to why I still really like his character, even though the game hasn't really done anything with him for like 4 years - because with him, it doesn't feel like a flaw.
Genshin doesn't like advancing character arcs, with rare exceptions involving pivotal moments in the archon quests. They prefer to leave the characters static as they are, so they can be pulled out and advertised for events whenever needed. With certain characters, when their plot threads remain unaddressed, and the game endeavors to shove their arcs to the side and bury them under the rug, it can be frustrating - I start to feel like what I liked about them was more their potential than anything that was actually executed. But Venti manages to avoid this, because if he refuses to talk about his problems, if he stays the same from year to year, then this tracks, that is exactly his problem. It's doesn't scan as out of character behavior, or the writers not wanting to touch it. His reasons to stay the same are spelled out in the text. I don't think this was an intentional choice by the writers, but it has led to an interesting result where the tendencies of the story feel justified.