fastapi: Unable to catch `Exception` via exception_handlers since FastAPI 0.70.0

First Check

• I added a very descriptive title to this issue.
• I used the GitHub search to find a similar issue and didn’t find it.
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• I already checked if it is not related to FastAPI but to Pydantic.
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Example Code

################################################
#
# Pay attention: below is Python 3.10 syntax
#
################################################

from fastapi import FastAPI, Request
from fastapi.responses import JSONResponse
from pydantic import ValidationError

async def internal_server_error(request: Request, exc: Exception | ValidationError) -> "JSONResponse":
    return JSONResponse(content={"detail": "Internal Server Error"}, status_code=500)

app = FastAPI(
    exception_handlers={
        Exception: internal_server_error,
        ValidationError: internal_server_error,
    },
)

@app.get("/call_me")
async def raise_exception() -> None:
    raise Exception("I am exception.")

Description

• Open the browser and call the endpoint: /call_me
• It returns plain text: Internal Server Error
• But I excepted it return JSON: {"detail": "Internal Server Error"}

Operating System

Linux

Operating System Details

No response

FastAPI Version

0.70.0

Python Version

Python 3.10.0

Additional Context

It works fine on FastAPI 0.68.2. Issue is also affected 0.69.0