...And it's already that way. There's plenty of lore regarding Dragonborn in Tymanther. There does not need to be equality of lore choice for every country, city, town and village in the entirety of the Realms. If you choose to make yourself a stranger in a strange land, you are not going to have as much local lore for your race as the locals do.
It's not enough to match 2024 5th edition's vibe
2024 5th edition's vibe for settings is either a Mos Eisley Cantina mix of species, classes, and backgrounds or a videogamey style faction fractionism where your choice of class, species, and backgrounds.
Either you run into Dragonborns all the time OR there is a lore reason why you don't run into Dragonborn here but do there.