Initial Checks

• I confirm that I'm using the latest version of Pydantic AI
• I confirm that I searched for my issue in https://github.com/pydantic/pydantic-ai/issues before opening this issue

Description

I was working on mirrored tests in test_agent.py and test_streaming.py for #3523 and discovered there's a difference in sync and streaming version for test_early_strategy_with_external_tool_call test.

Streaming version: link;
Sync version: link;

Both tests have the same input, but the behavior is different (both tests pass).
In streaming, defer tool is handled as final output in this part.
But in sync, the output tool becomes the final output in _agent_graph.

Example Code

https://gist.github.com/Danipulok/04ccb71269064e0bae8963f6e99884ff

Python, Pydantic AI & LLM client version

Python 3.13.4
pydantic==2.12.4
pydantic-ai==1.25.1