Move the last four inline domains out of lib/api.ts into per-domain slices,
each owning its types + method slice. The barrel now holds ZERO endpoint logic
and zero types of its own — it only re-exports core's HTTP machinery, re-exports
each domain's types, and spreads the 15 slices into the single `api` object.
A new endpoint therefore has nowhere to land but a domain module. The `api`
shape and all call sites are unchanged (every req/beacon call byte-identical
to dev; no method dropped, no key collision).