refactor(gateway): reuse looks_like_telegram_private_chat_id helper

The handoff seed path inlined its own int(chat_id) > 0 private-chat
check; delivery.py already had the identical heuristic. Promote it to
a public name and reuse it from both sites instead of duplicating.

cron/scheduler.py

@@ -1245,13 +1245,13 @@ def _deliver_result(job: dict, content: str, adapters=None, loop=None) -> Option
                 DeliveryRouter,
                 DeliveryTarget,
                 _looks_like_int,
-                _looks_like_telegram_private_chat_id,
+                looks_like_telegram_private_chat_id,
             )
 
             is_private_dm_topic = (
                 platform == Platform.TELEGRAM
                 and thread_id is not None
-                and _looks_like_telegram_private_chat_id(str(chat_id))
+                and looks_like_telegram_private_chat_id(str(chat_id))
                 and _looks_like_int(str(thread_id))
             )
             if is_private_dm_topic:

gateway/delivery.py

@@ -59,7 +59,14 @@ from .session import SessionSource
 from .dead_targets import DeadTargetRegistry
 
 
-def _looks_like_telegram_private_chat_id(chat_id: Optional[str]) -> bool:
+def looks_like_telegram_private_chat_id(chat_id: Optional[str]) -> bool:
+    """True when ``chat_id`` is a positive int — Telegram's private-chat shape.
+
+    Telegram private chats use positive chat IDs; groups/channels/supergroups
+    use negative IDs. This is the single source of truth for that heuristic,
+    reused by the handoff seed path in ``gateway/run.py`` so handoff-created
+    DM topics key the same way as inbound DM-topic messages.
+    """
     if chat_id is None:
         return False
     try:
@@ -467,7 +474,7 @@ class DeliveryRouter:
             target_thread_id = target.thread_id
             is_named_telegram_private_topic = (
                 target.platform == Platform.TELEGRAM
-                and _looks_like_telegram_private_chat_id(target.chat_id)
+                and looks_like_telegram_private_chat_id(target.chat_id)
                 and not _looks_like_int(target_thread_id)
                 and "thread_id" not in send_metadata
                 and "message_thread_id" not in send_metadata
@@ -490,7 +497,7 @@ class DeliveryRouter:
                 send_metadata["telegram_dm_topic_created_for_send"] = True
             elif (
                 target.platform == Platform.TELEGRAM
-                and _looks_like_telegram_private_chat_id(target.chat_id)
+                and looks_like_telegram_private_chat_id(target.chat_id)
                 and "thread_id" not in send_metadata
                 and "message_thread_id" not in send_metadata
                 and not has_explicit_direct_topic

gateway/run.py

@@ -1676,7 +1676,7 @@ from gateway.session import (
     build_session_key,
     is_shared_multi_user_session,
 )
-from gateway.delivery import DeliveryRouter
+from gateway.delivery import DeliveryRouter, looks_like_telegram_private_chat_id
 from gateway.authz_mixin import GatewayAuthorizationMixin
 from gateway.kanban_watchers import GatewayKanbanWatchersMixin
 from gateway.slash_commands import GatewaySlashCommandsMixin
@@ -6823,12 +6823,10 @@ class GatewayRunner(GatewayAuthorizationMixin, GatewayKanbanWatchersMixin, Gatew
         # handoff turn binds a generic `thread` session key while real replies
         # arrive on a `dm` session key.
         home_chat_id = str(home.chat_id)
-        is_telegram_private_chat = False
-        if platform == Platform.TELEGRAM:
-            try:
-                is_telegram_private_chat = int(home_chat_id) > 0
-            except (TypeError, ValueError):
-                is_telegram_private_chat = False
+        is_telegram_private_chat = (
+            platform == Platform.TELEGRAM
+            and looks_like_telegram_private_chat_id(home_chat_id)
+        )
 
         if new_thread_id and not is_telegram_private_chat:
             dest_chat_type = "thread"