fix(agent-loop): park empty turn batches, keep max-tokens sticky, and settle headless at idle

- turn boundary now returns false for an empty admitted batch (claimed
  input removed before the wake) instead of opening a turn and spending a
  model call on nothing; the step boundary already had the symmetric guard.
- a max-token step stays sticky when steering or injected work continues
  the turn: a later completed step no longer downgrades the outcome,
  matching the TurnEndReasonMap contract.
- session/queue wire schema accepts the context placement (previously the
  zod union rejected injected-context snapshots wholesale and the client
  silently dropped the whole frame); schema tests cover all placements.
- headless runs settle at whole-agent idle instead of the first turn/end,
  honoring the one-shot idle-to-idle contract.
- flush JSDoc names the real callers (checkpoint policy, goal-session,
  teardown, self-flushing consumers); apiproxy zh README loses its stale
  duplicate history section; ACP note/README record the delivered error
  rejection and turnless-cancelled behaviors.

packages/host/apiproxy/src/api/events.schema.ts

@@ -54,7 +54,7 @@ export const muxFrameSchema = z.discriminatedUnion('type', [
     sessionId: sessionIdSchema,
     items: z.array(z.object({
       id: messageIdSchema,
-      placement: z.union([z.literal('queued'), z.literal('steering')]),
+      placement: z.union([z.literal('queued'), z.literal('steering'), z.literal('context')]),
       message: messageSchema,
     })),
   }),