FastAPI: dependency_overrides does not override dependency in @app.on_event

I am facing an issue with FastAPI and Depends.
The snippet below contains two dependency_overrides statements, one in a @app.get the other in @app.on_event. While first tests runs through the other test fails:

from fastapi import Depends, FastAPI
from fastapi.testclient import TestClient

app = FastAPI()
values = {}


def startup_parameters():
    return {
        "foo": None,
        "bar": None
    }

def update_parameters():
    return {
        "foo": 1,
        "bar": 2
    }

def override_parameters():
    return {
        "foo": 5,
        "bar": 10
    }


@app.on_event("startup")
async def on_startup(commons: dict = Depends(startup_parameters)) -> None:
    global values
    values = commons

@app.get("/update/")
async def set_items(commons: dict = Depends(update_parameters)) -> None:
    global values
    values = commons

@app.get("/items/")
async def read_items():
    return values

# Test runs
def test_update_override():
    with TestClient(app) as client:
        app.dependency_overrides[update_parameters] = override_parameters
        client.get("/update/")
        response = client.get("/items/")
        assert response.json() == {
            "foo": 5,
            "bar": 10,
        }

# Test fails
def test_startup_override():
    with TestClient(app) as client:
        app.dependency_overrides[startup_parameters] = override_parameters
        response = client.get("/items/")
        assert response.json() == {
            "foo": 5,
            "bar": 10,
        }

Looking at FAST-API Documentation (https://fastapi.tiangolo.com/advanced/advanced-dependencies/) it seems to me that dependency injection is implemented for routes but not for events. But maybe there is a workaround for it.

Thanks a lot in advance...