I would have Species, Culture, and a third thing (maybe Profession) covering the ground of Race and Background in the PHB (more or less).
Species would be the races from the PHB (but broken down a bit, although not to the extent of PF2), and any cultural things (weapon training etc) removed.
Culture would be things like Mountain Stronghold, Plains Agrarian, Plains Horse Nomad. Generic, but with a sidebar on creating custom Cultures for specific settings.
Professions would be the the elements of background that have not been already stolen by Culture, mostly.
EDIT: Species and Profession would provide (flexible) ability score bonuses. Culture would not, for the reasons @Crimson Longinus outlines.
_
glass.