There are two different ways a race could be "official": it could be "official" in the sense of fully-tested and legal for sanctioned organized play campaigns, and it could be "official" in the sense of being published in 1st-party material from Wizards of the Coast. Which one is relevant depends on why you're looking for an "official" race.
BR: Basic Rules, Chapter 2: Races
SRD: System Reference Document, 5e, "Races" at p. 3-7
PHB: Player's Handbook, Chapter 2: Races
DMG: Dungeon Master's Guide, "Creating New Character Options" at p. 285-287
AI: Acquisitions Incorporated, "New Race: Verdan" at p. 72-74
EE: Elemental Evil Player's Companion, Chapter 1: Races
GGR: Guildmaster's Guide to Ravnica, p. 12-21
MToF: Mordenkainen's Tome of Foes, throughout Chapters 1-5
MOoT: Mythic Odesseys of Theros, Chapter 1 > Races
LR: Locathah Rising, an Extra Life fundraiser from WotC
OGA: One Grung Above, an Extra Life fundraiser from WotC
PotA: Princes of the Apocalypse, Appendix A: Genasi
PS:ZEN: Plane Shift: Zendikar, Races of Zendikar at p. 7
PS:INN: Plane Shift: Innistrad, Life on Innistrad at p. 7
PS:KLD: Plane Shift: Kaladesh, Races of Kaladesh at p. 15
PS:AKH: Plane Shift Amonkhet, Races of Amonkhet at p. 12
Note that Plane Shift occupies a strange shade-of-grey space: it's "compatible with" D&D, published by WotC, but written by the Magic: the Gathering team instead of the D&D team (though the author of all of them was a former D&D team member). Notably, it comes with a disclaimer substantially similar to the one provided with UA articles:
The game mechanics in this supplement are usable in your D&D campaign but are not fully tempered by playtests and design iterations. For these reasons, material in this supplement is not legal in D&D Organized Play events.
SCAG: Sword Coast Adventurer's Guide, Chapter 3: Races of the Realms
TP: The Tortle Package, an Extra Life fundraiser from WotC
UA: Unearthed Arcana articles, link and name specific article when listing
UA articles are presented on WotC's website with the following notice:
You can think of the material presented in this series as similar to the first wave of the fifth edition playtest. These game mechanics are in draft form, usable in your campaign but not fully tempered by playtests and design iterations. They are not officially part of the game. For these reasons, material in this column is not legal in D&D Organized Play events.
VOLO: Volo's Guide to Monsters, Chapter 2: Character Races
WGtE: Wayfinder's Guide to Eberron, Chapter 3: Races of Eberron
E:RftLW: Eberron: Rising from the Last War, Chapter 1: Character Creation
Note that Wayfinder's Guide to Eberron and Eberron: Rising from the Last War now redundantly feature most of the same new races, though the latter reprints the goblin, bugbear, and hobgoblin races, and includes a new version of the orc race. WGtE was originally published as a "living document", and was later updated with the versions of the included races as they appear in E:RftLW.
EGtW: Explorer's Guide to Wildemount, Chapter 4: Character Options, Races
Best Answer
Sources:
Artificer (WGtE, E:RftLW, TCoE)
Artificer Specialists:
Barbarian (SRD, PHB)
Primal Paths:
Bard (SRD, PHB)
Bard Colleges:
Cleric (BR, SRD, PHB)
Cleric Domains:
Druid (SRD, PHB)
Druid Circles:
Fighter (BR, SRD, PHB)
Fighter Archetypes:
Monk (SRD, PHB)
Monastic Traditions:
Paladin (SRD, PHB)
Sacred Oaths:
Ranger (SRD, PHB)
Ranger Archetypes:
Rogue (BR, SRD, PHB)
Roguish Archetypes:
Sorcerer (SRD, PHB)
Sorcerous Origins:
Warlock (SRD, PHB)
Otherworldly Patrons:
Wizard (BR, SRD, PHB)
Arcane Traditions:
D&D Beyond has a nicely formatted reference for all of the available classes/races/etc. Subclass and subrace information is also available by looking at the parent class or race's details. It should be noted that the free access materials do not include much outside of the D&D Basic Rules. They do offer other books' content, but that content must be purchased separately.
D&D Beyond
Classes Page
Races Page
1 These subclasses are included in the DMG and can be used only with the consent of the DM because they are generally made to be used for NPCs only or only in special DM-granted circumstances. However, the DM may choose to make these subclass options more generally available.