Fix tagged discriminated union not recognized as body field

Discussed in https://github.com/fastapi/fastapi/discussions/12941

fastapi/_compat.py

@@ -572,6 +572,9 @@ def field_annotation_is_complex(annotation: Union[Type[Any], None]) -> bool:
     if origin is Union or origin is UnionType:
         return any(field_annotation_is_complex(arg) for arg in get_args(annotation))
 
+    if origin is Annotated:
+        return field_annotation_is_complex(get_args(annotation)[0])
+
     return (
         _annotation_is_complex(annotation)
         or _annotation_is_complex(origin)

tests/test_union_body_discriminator.py

@@ -0,0 +1,57 @@
+from typing import Any, Dict, Union
+
+import pytest
+from fastapi import FastAPI
+from fastapi.testclient import TestClient
+from typing_extensions import Annotated
+
+from .utils import needs_pydanticv2
+
+
+@pytest.fixture(name="client")
+def get_client() -> TestClient:
+    from pydantic import BaseModel, Discriminator, Tag
+
+    app = FastAPI()
+
+    class FirstItem(BaseModel):
+        value: str
+        price: int
+
+    class OtherItem(BaseModel):
+        value: str
+        price: float
+
+    def get_discriminator_value(v: Any) -> str:
+        if isinstance(v, dict):
+            return v.get("value")
+        return v.value
+
+    Item = Annotated[
+        Union[
+            Annotated[FirstItem, Tag("first")],
+            Annotated[OtherItem, Tag("other")],
+        ],
+        Discriminator(get_discriminator_value),
+    ]
+
+    @app.post("/items/")
+    def save_union_body_discriminator(item: Item) -> Dict[str, Any]:
+        return {"item": item}
+
+    client = TestClient(app)
+    return client
+
+
+@needs_pydanticv2
+def test_post_item(client: TestClient) -> None:
+    response = client.post("/items/", json={"value": "first", "price": 100})
+    assert response.status_code == 200, response.text
+    assert response.json() == {"item": {"value": "first", "price": 100}}
+
+
+@needs_pydanticv2
+def test_post_other_item(client: TestClient) -> None:
+    response = client.post("/items/", json={"value": "other", "price": 100.5})
+    assert response.status_code == 200, response.text
+    assert response.json() == {"item": {"value": "other", "price": 100.5}}