Dahlia wonders why he got the hydro vision and jokes it's because Barbatos doesn't need to watch over him; however, I see it easily. The hydro vision is given to those with a strong sense of duty, leadership, and devotion to those they lead.
When Dahlia began his path, he did not work for the church; in fact, he despised the idea. Yet so bored out of his mind, the winds kept blowing him back. And he would help when needed, but run away whenever the work was done.
Venti questioned him on this, and Dahlia explained the church felt terrible from the monotone prayers, significant time on the ceremony of it all. To Dahlia, this was the greatest enemy of all: boredom. The church was a solemn and gloomy place that he was dragged to in his childhood, and he looked for any reason to escape it. And yet Barbatos, hearing this, asks, "If there was a way to make the rituals more interesting, would he consider it then? For instance, what if he were to help transmit the Anemo Archon's guidance to his flock?" and Dahlia accepts.
Still, the church was not his dream or his idea of freely running the streets looking for trouble. Dahlia rebels against every aspect of the church, from the robes, which he took many layers off of, to how the daily prayers are conducted.
Until he realized his people need a deacon who is committed. Someone who was not flying by the seat of their pants. Dahlia knew nothing of the prayers they all believed in. But he sat down these dizzying scriptures he didn't like and knew were not the will of Barbatos, but for their shared flock, he learned. He learned every single scripture from the front to the back of the Anemo Archon. His words became more solemn as he always rejected. And then appeared a hydro vision, and Dahlia says, "Perhaps fate smiles on those who are most diligent?"
Meaning there is no freedom for Dahlia in his role. Sure he can change his outfit and run the streets of Mondstadt but he has to return to lead prayer and the church can only be so exciting. More voice lines suggests he is still stifled by it and longs desperately to seek outside of Mondsadt, but he won't set foot away from the dandelion fields until his flock no longer needs him. His duty overrides his freedom. And that is why he was given a hydro vision, not an anemo one.