Refs #34118 -- Adopted asgiref coroutine detection shims.

Thanks to Mariusz Felisiak for review.

docs/topics/async.txt

@@ -28,10 +28,10 @@ class-based view, this means declaring the HTTP method handlers, such as
 
 .. note::
 
-    Django uses ``asyncio.iscoroutinefunction`` to test if your view is
+    Django uses ``asgiref.sync.iscoroutinefunction`` to test if your view is
     asynchronous or not. If you implement your own method of returning a
-    coroutine, ensure you set the ``_is_coroutine`` attribute of the view
-    to ``asyncio.coroutines._is_coroutine`` so this function returns ``True``.
+    coroutine, ensure you use ``asgiref.sync.markcoroutinefunction`` so this
+    function returns ``True``.
 
 Under a WSGI server, async views will run in their own, one-off event loop.
 This means you can use async features, like concurrent async HTTP requests,

docs/topics/http/middleware.txt

@@ -312,7 +312,7 @@ If your middleware has both ``sync_capable = True`` and
 ``async_capable = True``, then Django will pass it the request without
 converting it. In this case, you can work out if your middleware will receive
 async requests by checking if the ``get_response`` object you are passed is a
-coroutine function, using ``asyncio.iscoroutinefunction``.
+coroutine function, using ``asgiref.sync.iscoroutinefunction``.
 
 The ``django.utils.decorators`` module contains
 :func:`~django.utils.decorators.sync_only_middleware`,
@@ -331,13 +331,13 @@ at an additional performance penalty.
 
 Here's an example of how to create a middleware function that supports both::
 
-    import asyncio
+    from asgiref.sync import iscoroutinefunction
     from django.utils.decorators import sync_and_async_middleware
 
     @sync_and_async_middleware
     def simple_middleware(get_response):
         # One-time configuration and initialization goes here.
-        if asyncio.iscoroutinefunction(get_response):
+        if iscoroutinefunction(get_response):
             async def middleware(request):
                 # Do something here!
                 response = await get_response(request)