Elves: They’ll be there, but I’m not sure quite how yet. Maybe some wood-elves with a Hobbit vibe to them. They will probably be rare, and in isolated places, at least within the Land of Azurth.
Dwarves: There probably will be something pretty much like the D&D standard dwarf, but these guys will be rare. The more common dwarf type will be something like the Kologor dwarves of Hollow World, i.e. the beer-drinking, ninepin-playing variety. There may also be something like the Dark Sun dwarf in the arid parts of Sang.
Halflings: Halfings will be in abundance, though they may not be distinguished from other “little people” races as much as in standard D&D. I suspect they may well have a chance of unusual traits like on the Dwarf Land trait tables.
Gnomes: Gnomes will just be another variety of little folk, distinguished only by their aptitude as tinkerers. There will be a number of them clustered around Viola, the Clockwork Princess of Yanth.
Tieflings: These will be the majority of the population in Daemonland beyond the borders of Azurth. They’ll show up elsewhere, but rarely. In appearance, they’ll typically be more DiTerlizzi than the 5e illustations.
Dragonborn: Though they may be a bit different, they’ll be found in Sang, but probably not elsewhere.