Fix bug where we wedge media plugins if clients disconnect early (#13660)

We incorrectly didn't use the returned `Responder` if the client had
disconnected, which meant that the resource used by the Responder
wasn't correctly released.

In particular, this exhausted the thread pools so that *all* requests
timed out.

changelog.d/13660.bugfix

@@ -0,0 +1 @@
+Fix bug where we wedge media plugins if clients disconnect early. Introduced in v1.22.0.

synapse/rest/media/v1/_base.py

@@ -254,20 +254,22 @@ async def respond_with_responder(
         file_size: Size in bytes of the media. If not known it should be None
         upload_name: The name of the requested file, if any.
     """
+    if not responder:
+        respond_404(request)
+        return
+
+    # If we have a responder we *must* use it as a context manager.
+    with responder:
         if request._disconnected:
             logger.warning(
                 "Not sending response to request %s, already disconnected.", request
             )
             return
 
-    if not responder:
-        respond_404(request)
-        return
-
         logger.debug("Responding to media request with responder %s", responder)
         add_file_headers(request, media_type, file_size, upload_name)
         try:
-        with responder:
+
             await responder.write_to_consumer(request)
         except Exception as e:
             # The majority of the time this will be due to the client having gone