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

@@ -254,30 +254,32 @@ 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 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
-        # away. Unfortunately, Twisted simply throws a generic exception at us
-        # in that case.
-        logger.warning("Failed to write to consumer: %s %s", type(e), e)
+    # 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
 
-        # Unregister the producer, if it has one, so Twisted doesn't complain
-        if request.producer:
-            request.unregisterProducer()
+        logger.debug("Responding to media request with responder %s", responder)
+        add_file_headers(request, media_type, file_size, upload_name)
+        try:
+
+            await responder.write_to_consumer(request)
+        except Exception as e:
+            # The majority of the time this will be due to the client having gone
+            # away. Unfortunately, Twisted simply throws a generic exception at us
+            # in that case.
+            logger.warning("Failed to write to consumer: %s %s", type(e), e)
+
+            # Unregister the producer, if it has one, so Twisted doesn't complain
+            if request.producer:
+                request.unregisterProducer()
 
     finish_request(request)