fix(background_process): do not consume the delivery budget on transient wake-up refusals

start_session_turn() answers 409 retryable=True while the Agent runtime is
stale, 409 process_wakeup_paused while wake-ups are paused, and 409 with
active_stream_id while the session is busy with another turn. The bridge
released the durable claim as a plain failure each time, so a burst of
refusals within seconds terminally dropped a completion whose origin session
was alive and waiting.

release_async_delegation_delivery(..., retryable=True) now forwards the
refund to an Agent core whose release_event_delivery() accepts the
`retryable` keyword (NousResearch/hermes-agent#120028), detected through
inspect.signature, and falls back to the historical plain release on an
older core. Hard rejections keep the bounded budget.

api/process_event_utils.py

@@ -3,6 +3,7 @@ from __future__ import annotations
 
 from collections import OrderedDict
 from dataclasses import dataclass
+import inspect
 import logging
 import math
 import re
@@ -451,16 +452,46 @@ def complete_async_delegation_delivery(
     _mark_legacy_async_delivery_complete(claim.delegation_id)
 
 
+def _release_accepts_retryable(release_fn: Any) -> bool:
+    """Whether the core ``release_event_delivery`` supports ``retryable=``.
+
+    Older Agent cores predate the keyword; calling them with it would raise
+    ``TypeError`` and skip the release entirely.
+    """
+    try:
+        params = inspect.signature(release_fn).parameters
+    except (TypeError, ValueError):
+        return False
+    if "retryable" in params:
+        return params["retryable"].kind in (
+            inspect.Parameter.KEYWORD_ONLY,
+            inspect.Parameter.POSITIONAL_OR_KEYWORD,
+        )
+    return any(p.kind is inspect.Parameter.VAR_KEYWORD for p in params.values())
+
+
 def release_async_delegation_delivery(
     evt: Any,
     claim: AsyncDelegationDeliveryClaim,
+    *,
+    retryable: bool = False,
 ) -> None:
-    """Release a failed claim so a later WebUI consumer can retry it."""
+    """Release a failed claim so a later WebUI consumer can retry it.
+
+    ``retryable=True`` tells the core the refusal was transient, so the claimed
+    attempt is refunded instead of counting against the bounded delivery
+    budget (``tools.async_delegation.release_event_delivery(...,
+    retryable=True)``). A core that predates the keyword gets a plain release:
+    the attempt is then consumed as before, never an exception.
+    """
     try:
         if claim.durable:
             from tools.async_delegation import release_event_delivery
 
-            release_event_delivery(evt, claim.claim_id)
+            if retryable and _release_accepts_retryable(release_event_delivery):
+                release_event_delivery(evt, claim.claim_id, retryable=True)
+            else:
+                release_event_delivery(evt, claim.claim_id)
     except Exception:
         logger.warning(
             "Failed to release durable async delegation delivery for %s",