My criticisms of the Dragonborn lore in the Forgotten Realms is 1) it’s tied to the Spellplague and whole Abeir-Toril continent switching shenanigans and 2) they’re just boring. They’re a stoic, proud, righteous warrior race. Basically Paladins, the species. And there should be more to them than just another stoic warrior race, we have two others of those in the Tritions and Goliaths, and they’re boring too. There are interesting concepts in their backstory, like having formerly being enslaved by dragons and since breaking free, and the whole “stranger in a strange land” trope is nice too. However, they come from an alternate universe without gods where they violently rebelled against their former masters that had ruled over them for thousands of years. They should be a bit more culturally alien and probably more anti-theistic and anti-authoritarian, instead of mainly anti-dragon. The Faerunian Dragonborn should have a culture of “no gods, no masters,” and see the Monarchs in Faerun in a similar view to their old tyrannical Dragonlords. Like, why is Tymanthar a monarchy? Why does it have secret police? Why do the Dragonborn have clans? Why are they tolerant of Tieflings and other marginalized races when their tyrannical government is a controlled by an authoritarian warlord? It just doesn’t make sense to me. I guess that’s criticism #3. Their culture doesn’t make sense given their history.
There should be lore on how Dragonborn of different ancestries are treated and used by Dragonborn society. Gold and Red Dragonborn are more likely to be bakers and blacksmiths, White and Silver Dragonborn invented ice cream, Blue and Bronze Dragonborn discovered artifice and electricity, and so on. Maybe as a way of distancing themselves from their former masters or as a symbol of rebellion, the Dragonborn of certain ancestries reject the stereotypes tied to their scale color. Red Dragonborn try to be charitable and cool-headed, Green Dragonborn try to be honest and forthcoming, Copper Dragonborn despise humor of all kinds, especially pranks. They still define themselves in relation to the Dragons, but now with opposition to the Dragons having a major effect on their culture. If a Dragonborn laughs a lot, another Dragonborn might say something along the lines of “feeling a bit copper, are you?”
Additionally, new Dragonborn lore should have some connection to the First World. Maybe Dragonborn were the first humanoid race to be created and also have echoes in different worlds of the Material Plane. Dragonborn might have superstitions related to this (DID is seen as the personalities of the Dragonborn’s echoes temporarily taking over their body, schizophrenia is viewed as seeing/hearing things from different worlds through the eyes and ears of your echoes, etc). Echo Knights might form a prestigious ancient Dragonborn order of knights, possibly in their rebellions against their Dragonlords. Maybe Eberron Dragonborn of the Blood of Vol believe that unlocking the Divinity Within requires gaining Dragonsight, possibly also thinking only Dragonborn can accomplish this. Dragonborn Warlocks might enter into pacts with Greatwyrm Dragons as a way of learning how to get Echo magic.