Include the stable identifier for MSC3288. (#11187)

Includes both the stable and unstable identifier to store-invite
calls to the identity server. In the future we should remove the
unstable identifier.

changelog.d/11187.feature

@@ -0,0 +1 @@
+Support the stable room type field for [MSC3288](https://github.com/matrix-org/matrix-doc/pull/3288).

synapse/handlers/identity.py

@@ -879,6 +879,8 @@ class IdentityHandler:
         }
 
         if room_type is not None:
+            invite_config["room_type"] = room_type
+            # TODO The unstable field is deprecated and should be removed in the future.
             invite_config["org.matrix.msc3288.room_type"] = room_type
 
         # If a custom web client location is available, include it in the request.