REST API: Introduce baby API to the world.



Baby API was born at 2.8KLOC on October 8th at 2:30 UTC. API has lots

of growing to do, so wish it the best of luck.



Thanks to everyone who helped along the way:



Props rmccue, rachelbaker, danielbachhuber, joehoyle, drewapicture,

adamsilverstein, netweb, tlovett1, shelob9, kadamwhite, pento,

westonruter, nikv, tobych, redsweater, alecuf, pollyplummer, hurtige,

bpetty, oso96_2000, ericlewis, wonderboymusic, joshkadis, mordauk,

jdgrimes, johnbillion, jeremyfelt, thiago-negri, jdolan, pkevan,

iseulde, thenbrent, maxcutler, kwight, markoheijnen, phh, natewr,

jjeaton, shprink, mattheu, quasel, jmusal, codebykat, hubdotcom,

tapsboy, QWp6t, pushred, jaredcobb, justinsainton, japh, matrixik,

jorbin, frozzare, codfish, michael-arestad, kellbot, ironpaperweight,

simonlampen, alisspers, eliorivero, davidbhayes, JohnDittmar, dimadin,

traversal, cmmarslender, Toddses, kokarn, welcher, and ericpedia.



Fixes #33982.

