FastAPI `uninstrument` disallows adding more middlewares with `fastapi@>=0.91` and `starlette@>=0.24`

Uninstrument is breaking subsequent calls to add_middleware due to recent changes in starlette https://github.com/encode/starlette/pull/2017 and latest version of fastapi@>=0.91.

Call to build_middleware_stack makes an instance of FastAPI and starelette to think that application is already running

Describe your environment

Python 3.9.9

opentelemetry-distro = "^0.41b0"
opentelemetry-exporter-otlp = "^1.20.0"
opentelemetry-instrumentation-aws-lambda = "^0.41b0"
opentelemetry-instrumentation-dbapi = "^0.41b0"
opentelemetry-instrumentation-logging = "^0.41b0"
opentelemetry-instrumentation-sqlite3 = "^0.41b0"
opentelemetry-instrumentation-urllib = "^0.41b0"
opentelemetry-instrumentation-wsgi = "^0.41b0"
opentelemetry-instrumentation-asgi = "^0.41b0"
opentelemetry-instrumentation-fastapi = "^0.41b0"
opentelemetry-instrumentation-grpc = "^0.41b0"
opentelemetry-instrumentation-httpx = "^0.41b0"
opentelemetry-instrumentation-requests = "^0.41b0"
opentelemetry-instrumentation-sqlalchemy = "^0.41b0"
opentelemetry-instrumentation-urllib3 = "^0.41b0"

Steps to reproduce
Describe exactly how to reproduce the error. Include a code sample if applicable.

from starlette.middleware.cors import CORSMiddleware
from opentelemetry.instrumentation.fastapi import FastAPIInstrumentor

app = FastAPI(...)

FastAPIInstrumentor.uninstrument_app(app)

app.add_middleware(
    CORSMiddleware,
    allow_credentials=True,
    allow_methods=["*"],
    allow_headers=["*"],
)

What is the expected behavior?
What did you expect to see?

FastAPIInstrumentor.uninstrument_app should not break ability to add more middlewares

What is the actual behavior?
What did you see instead?

Application crashes:

  File "/xxx/.venv/lib/python3.9/site-packages/starlette/applications.py", line 139, in add_middleware
    raise RuntimeError("Cannot add middleware after an application has started")

Additional context
Add any other context about the problem here.

Start in instrumentation/opentelemetry-instrumentation-fastapi/src/opentelemetry/instrumentation/fastapi/init.py at build_middleware_stack and review FastAPIInstrumentor.uninstrument_app alongside the linked Starlette change. Reproduce with the provided FastAPI and CORSMiddleware example using FastAPI >=0.91 and Starlette >=0.24. Done means uninstrument_app no longer prevents a later app.add_middleware call.