[Bug] for sse Server-Sent Events, opentelemetry-instrumentation-flask server span time is less than real response end

Describe your environment

OS: (e.g, Ubuntu)
Python version: (e.g., Python 3.8.10)
Package version: (e.g., 0.46.0)

What happened?

When I use opentelemetry-instrumentation-flask to get flask sse span, the server span end before the sse response end, that makes flask sse server span time is incorrect. Did anyone solve this problem ?

from flask import Flask, Response
import time
import os
import flask
from opentelemetry.instrumentation.flask import FlaskInstrumentor, _ENVIRON_SPAN_KEY
from opentelemetry import trace
from opentelemetry.sdk.trace import TracerProvider
from opentelemetry.sdk.trace.export import ConsoleSpanExporter, BatchSpanProcessor
from werkzeug.local import LocalProxy
from opentelemetry.trace import get_current_span
app = Flask(__name__)

# 初始化追踪提供者和导出器
provider = TracerProvider()
console_exporter = ConsoleSpanExporter()
provider.add_span_processor(BatchSpanProcessor(console_exporter))
trace.set_tracer_provider(provider)

# 初始化 FlaskInstrumentor 并应用到 Flask 应用
FlaskInstrumentor().instrument_app(app)


# 定义一个生成器，用于流数据
def event_stream():
    for i in range(1, 5):
        # 每次发送消息（遵循 SSE 数据格式）
        yield f"data: Server Time {time.ctime()}\n\n"
        time.sleep(1)  # 每秒发送一次


@app.route('/stream')
def stream():
    # 返回流式响应
    response = Response(event_stream(), content_type='text/event-stream')
    response.headers["test"] = "test"
    return response


if __name__ == '__main__':
    app.run(debug=True)

Steps to Reproduce

code

Expected Result

code

Actual Result

code

Additional context

code

Would you like to implement a fix?

None

Start by reproducing the provided Flask SSE example, focusing on FlaskInstrumentor().instrument_app(app) and the /stream entry point. Trace when the server span ends relative to the event_stream response, and consider the issue complete when the span duration includes the full streamed response.