broker: recv_batch(max) — drain a bursty inbox in one round-trip

CLAUDE.md

@@ -183,6 +183,29 @@ read them à la carte.
 In-flight or recent context that hasn't earned a section yet.
 Prune freely.
 
+- **Just landed:** inbox batching via `recv_batch(max)`. New
+  MCP tool on both agent + manager surfaces pops up to `max`
+  pending messages in a single round-trip (server-side cap
+  32, `max = 0` short-circuits). Same delivery + ack
+  bookkeeping as `recv`: every popped row is marked
+  `delivered_at = NOW`, tracked on the per-recipient
+  `unacked_ids` list (so the next `AckTurn` closes them out),
+  and tagged `redelivered: true` if it was resurfaced by
+  `RequeueInflight`. Wake prompt's pending-inbox hint
+  rewritten to recommend `recv_batch(max: N)` instead of N
+  consecutive `recv`s. Wire: new
+  `AgentRequest::RecvBatch { max }` /
+  `AgentResponse::Batch { messages: Vec<DeliveredMessage> }`
+  (+ manager mirror) and a new `DeliveredMessage` struct in
+  `hive-sh4re` shared by both. `format_recv_batch` on the
+  mcp side renders the popped list with per-message
+  redelivery banners + `---` separators; empty batch
+  collapses to "(empty)" like single `recv`. 4 new broker
+  tests cover FIFO + cap, empty-when-idle, zero-max
+  short-circuit, and redelivered-flag propagation. Closes
+  the "inbox batching hint" item from the ergonomics
+  wishlist — the hint that was already in `format_wake_prompt`
+  is now actionable in one tool call instead of N.
 - **Just landed:** lease-style message delivery / no-drop
   on turn fail. The `messages` table gained an `acked_at`
   column (idempotent ALTER + backfill = `delivered_at` so