[BUG] dash 4.2.0-Dash 4.3.0rc0 POST deadlock #3801

# POST — times out (BUG)
curl -s -m 5 -X POST http://127.0.0.1:9999/api/echo \
    -H "Content-Type: application/json" \
    -d '{"hello":"world"}'

import os
from dash import Dash, html
from fastapi import FastAPI, Request
from fastapi.responses import JSONResponse

fastapi_app = FastAPI()
dash_app = Dash(__name__, server=fastapi_app)
dash_app.layout = html.Div("Dash is running")

@fastapi_app.get("/api/echo")
async def echo_get():
    return JSONResponse({"method": "GET", "ok": True})

@fastapi_app.post("/api/echo")
async def echo_post(request: Request):
    body = await request.json()     # ← HANGS here
    return JSONResponse({"echo": body})

if __name__ == "__main__":
    dash_app.run(host="127.0.0.1", port=9999, debug=False)