docs: document auto_previous_response_id and drop stale error_handlers value list

PR #2117 added the `auto_previous_response_id` parameter to
`Runner.run`, `Runner.run_sync`, and `Runner.run_streamed` signatures
but did not document it in the `Args:` blocks (parameter appears in
`inspect.signature` but not in `inspect.getdoc`).

Add the missing `auto_previous_response_id` entry to each `Args:`
block. Drop the "Currently supports max_turns" enumeration from the
`error_handlers` docstrings (3 in `run.py`, 1 in
`run_config.py:RunOptions.error_handlers`) to avoid documenting a list
that will drift again as more handler kinds are added.

Author: ioleksiuk

src/agents/run.py

@@ -239,10 +239,13 @@ async def run(
                 Pass ``None`` to disable the turn limit.
             hooks: An object that receives callbacks on various lifecycle events.
             run_config: Global settings for the entire agent run.
-            error_handlers: Error handlers keyed by error kind. Currently supports max_turns.
+            error_handlers: Error handlers keyed by error kind.
             previous_response_id: The ID of the previous response. If using OpenAI
                 models via the Responses API, this allows you to skip passing in input
                 from the previous turn.
+            auto_previous_response_id: If True, enable Responses API response chaining
+                automatically for the first turn even when no
+                ``previous_response_id`` is supplied yet.
             conversation_id: The conversation ID
                 (https://platform.openai.com/docs/guides/conversation-state?api-mode=responses).
                 If provided, the conversation will be used to read and write items.
@@ -325,10 +328,13 @@ def run_sync(
                 Pass ``None`` to disable the turn limit.
             hooks: An object that receives callbacks on various lifecycle events.
             run_config: Global settings for the entire agent run.
-            error_handlers: Error handlers keyed by error kind. Currently supports max_turns.
+            error_handlers: Error handlers keyed by error kind.
             previous_response_id: The ID of the previous response, if using OpenAI
                 models via the Responses API, this allows you to skip passing in input
                 from the previous turn.
+            auto_previous_response_id: If True, enable Responses API response chaining
+                automatically for the first turn even when no
+                ``previous_response_id`` is supplied yet.
             conversation_id: The ID of the stored conversation, if any.
             session: A session for automatic conversation history management.
 
@@ -402,10 +408,13 @@ def run_streamed(
                 Pass ``None`` to disable the turn limit.
             hooks: An object that receives callbacks on various lifecycle events.
             run_config: Global settings for the entire agent run.
-            error_handlers: Error handlers keyed by error kind. Currently supports max_turns.
+            error_handlers: Error handlers keyed by error kind.
             previous_response_id: The ID of the previous response, if using OpenAI
                 models via the Responses API, this allows you to skip passing in input
                 from the previous turn.
+            auto_previous_response_id: If True, enable Responses API response chaining
+                automatically for the first turn even when no
+                ``previous_response_id`` is supplied yet.
             conversation_id: The ID of the stored conversation, if any.
             session: A session for automatic conversation history management.
 

src/agents/run_config.py

@@ -349,7 +349,7 @@ class RunOptions(TypedDict, Generic[TContext]):
     """The session for the run."""
 
     error_handlers: NotRequired[RunErrorHandlers[TContext] | None]
-    """Error handlers keyed by error kind. Currently supports max_turns."""
+    """Error handlers keyed by error kind."""
 
 
 __all__ = [