One of my favorite things I see artists do with Byleth is giving them different designs/outfits for each route in the same vein as Corrin’s Hoshido/Nohr classes in Fates. I honestly think one area FE3H fell short on was showing the differences between each version of Byleth - because you can’t convince me that they are just consistently the same every time despite the drastically different things they are fighting for.
I imagine Crimson Flower!Byleth is likely the most cold and aloof, and has the least amount of tolerance for bullshit. Not to say they are emotionally detatched - I also think they are obviously incredibly loyal and are willing to do nearly anything for those they love. I think this version of Byleth doesn’t shy away from using intimidation to their advantage - and while they still aren’t fond of the moniker “Ashen Demon”, they mind it the least here.
I interpret Azure Moon!Byleth as being the most honor-bound and morally rigid. Not to the degree of the rest of the Blue Lions, mind you, but their students rubbed off on them. They always go by a strict set of personal rules that nobody can quite seem to pinpoint, because they don’t always align with the standards of Faerghus or the Church of Serios. They obviously believe in the idea of redemption and are quick to extend that opportunity when possible. I also think this version of Byleth truly despises being called “Ashen Demon”.
I see Verdant Wind!Byleth as being far more eloquently spoken when they want to be, mostly due to the off-screen interactions with the Round Table. They are constantly questioning almost everything they are told for pretty obvious reasons, albeit usually internally or in the way of personal research. They are far more willing to be underhanded than the other two in the name of the greater good - potentially even more so than Claude himself, at least in certain areas. This Byleth is also the best at expressing/communicating their emotions - not by a large margin or anything, this is still Byleth, but there’s a notable difference.
And I’m sure there’s also changes in Silver Snow!Byleth, but I don’t really care about that route enough to analyze tbh. Maybe something about them having the most passion but the least sense of self?
For what it's worth your description of Verdant Byleth sounds really close to how I imagine them. Maybe that's a reflection more of my character onto them, but even in that case I'd say you're pretty good at guessing the types of players that choose the houses. So I'll accept this as canon. Also speaking of the differences between Byleth's I always like to think that M!Byleth more the quiet type but F!Byleth is more rough around the edges /"feral". They both have shades of that but I just think it's fun to give them tiny differences.
I actually disagree- I see SS Byleth as the most emotionally repressed and cold. It's the route where a major thing in the story is Byleth constantly being either unwilling or unable to make their own choices, constantly being override by their seniors Seteth and Gilbert, and being the only route where the Battle of Three Armies still happens but you do not take part. Instead, Byleth is essentially a figurehead for the Church's cause.
By contrast, Crimson Flower shows them and Edelgard regaining their humanity, culminating in them finally giving up their divinity and their heart beating for the first time. So I think CF! Byleth would be much more ebullient and given to displays of emotion than the other Byleths- (as emotional as Byleth ever gets, anyways, they still don't express their emotions outwardly very strongly). I think they would actually really dislike being called the Ashen Demon for this reason.
I generally agree with your assessment of VW Byleth- i definitely think Lorenz and Claude's diplomacy and more roundabout methods of problem solving would rub off.
(I have no strong feelings on your assessments of Azure Moon Byleth- I never ended up finishing either BL route, for reasons I will not get into here.)
