One-dimensional characters are nothing new to the Fire Emblem franchise - with so many characters, there is usually a focus on the main players (nobility and the player character) and a few dimensionless filler characters to fill out the roster.
Playing through Engage, even the nobility felt like filler. One of them likes to drink tea? Prepare for every one of her conversations to be about tea. Want to learn more about how much another princess likes meat? Just you wait - that is pretty much all she will be talking about. How about one of the prince's strength training and muscles? You are in luck - you'll get that... and a toss away character with the same muscle obsession.
Compare with Three Houses - every character had some kind of secret and depth to them, which increasingly became known through conversations and the story.
The one dimensionality of the characters is made worse by the almost singular way in which they interact with the player character. In prior games, you were a respected tactician, a beloved sibling, a teacher who comes to serve a lord. Folks that you might look to in battle - but who were still a part of the team and interacted with as a brother or sister in arms, a treasured advisor following one of the other characters
But in Engage? You are basically their god - and every single character treats you like it. There is no superior lord who confides in you as a trusted advisor. No people who treat you as an equal. You are their god and leader and they make sure to remind you at every turn.
All of which is incredibly disappointing given how fun the gameplay is - it is a Fire Emblem game, after all. But what sets Fire Emblem apart from other tactical games has always been the characters and their relationships - and this really fell flat on that front.