I believe the name for those were “dragoons”. I thought about it, but my understanding was they were armed with muskets. Since firing a rifle from horseback usually meant you missed, they would dismount before engaging. I suppose it’s not a stretch to have dragoons that only carried swords, but we also know that they had 5000 troops in that battle and even if they doubled up the riders that’s over 2000 horses. We saw, maybe 2 dozen in the retreat

Dragoons were a more recent incarnation. I believe there were other earlier ones.

Basically what went wrong with this scene in Reincarnated Aristocrat, though, is that they went for too much detail in a crowd scene that would have been much better off with less. If you look at older anime from the hand-drawn cell era, they didn’t try to individually animate every member of a large group like an army. Exaggerated atmosperic perspective and depth of field, plus judicious use of detail, reduced the parts of the army away from the main characters to a sort of dark mass with the occasional helmet or horse-leg movement—and that was okay, because we didn’t care enough about those people to focus on them individually. Currently there’s a fad for using computer animation to spam copies of the same model, often poorly animated, to make up the numbers, and it doesn’t work and tends to be very noticeable. Hopefully someone in Japan will eventually figure that out, and they’ll return to the more painterly approach.