What the Players Handbook calls "race" is inseparable from "culture".
Everything from language, to skill and weapon proficiencies, to ability improvements, to special traits, look like the same mechanics that backgrounds and feats grant. Certain mechanically loaded concepts, like vampire or dragon, work better as classes that advance across levels, or as feats with level prereqs.
Suppose "race" splits into: culture + species.
Essentially, "species" seems little more than a place on the character sheet to put "physical appearance", such as skin color and average height. Because skin color, hair color, and eye color, plus height and weight, are things that a player chooses arbitrarily anyway, according to personal taste and character concept, species itself doesnt matter mechanically.
Besides physical appearance, everything seems like optional choices that backgrounds can supply, including proficiencies in language, skill, tool, singular weapon, and non-combat minor-feature ribbon. Even horns or claws are a weapon proficiency, mechanically.
Certain mechanics relating to height and weight might imply mechanics. Small size disadvantages heavy weapons. Large might hypothetically grant a size bonus to damage, albeit not necessarily. For the most part, the player character can default to Medium size. Even a halfling player character can be a tall 4 feet, rather than the "average" 3 feet. An ogre player character might be unusuaully short at 7 feet, or else young and still growing. During character building at level 1, to be Large or Small is a player choice, that seems more like part of a feat, whether a benefit or a cost, that a player likes and chooses.
Similarly Speed modifiers, whether a benefit or cost, seems more like part of feat. Compare how Monk and Barbarian learn to walk faster.
Even Darkvision looks like a cantrip that any culture can learn. Compare how Warlocks learn how to do it.
Notice how a species that has tough, scaly, natural armor is only a feat. For the Dragonborn species, Dragon Hide (Xanathars) is an optional feat choice that a player may or may not want.
Even Wings work more like a feat, that according to other editions of D&D has a level prerequisite, or else like a prestige class or a path.
An ability score improvement comes from a feat, whether the feat grants +2 to one ability score, or +1 to two ability scores. A halffeats can swap with one of these +1s.
In sum, a "species" is simply a place on the character sheet to put physical appearance. Language is cultural, and depends on the setting. Everything else is cultural backgrounds that supply proficiencies and ribbons, ideals and flaws. Additionally, both species and backgrounds can suggest certain feats that a player might want to choose to further develop the concept of the species.
When designing a species, the flavor depends entirely on the setting. Each setting guide can supply a default version of a species that represents a "typical" member of the species within this setting and that preselects the choices of skin color and average height, plus mechanically an ability improvement, feat, and a "species background" that correlates with the species in this setting. The player can swap each of the mechanical units − feat, halffeat, proficiency/ribbon − for an other that is more desirable to individuate and personalize a character concept.