♻️(backend) pass the participant role in the LiveKit token

The backend previously passed an abstract is_admin_or_owner boolean
flag in the LiveKit token. That kept the frontend minimalistic and
saved it from having to handle role comparisons.

As we introduce more features that need to distinguish between the
room owner and admins, refactor the token to carry the role
directly. The frontend can then derive the relevant flags from a
richer piece of information.

src/backend/core/services/room_roles.py

@@ -4,7 +4,7 @@ Single entry point for changing a user's role on a room, used by:
 - the in-meeting endpoint (promote/demote a connected participant)
 - (more to come soon)
 
-`ResourceAccess` is the source of truth. The LiveKit `room_admin`
+`ResourceAccess` is the source of truth. The LiveKit `room_role`
 participant attribute is only a projection of it, synced best-effort.
 """
 
@@ -138,7 +138,7 @@ class RoomRoleService:
         livekit_synced = self._sync_livekit_role(
             room_name=room_name,
             participant_identity=str(participant_identity),
-            is_admin=role == models.RoleChoices.ADMIN,
+            role=str(role),
         )
 
         return {
@@ -147,7 +147,7 @@ class RoomRoleService:
         }
 
     @staticmethod
-    def _sync_livekit_role(room_name: str, participant_identity: str, is_admin: bool):
+    def _sync_livekit_role(room_name: str, participant_identity: str, role: str):
         """Mirror the role to the participant's LiveKit attributes.
 
         Best-effort: returns False on failure instead of raising, so callers
@@ -157,7 +157,7 @@ class RoomRoleService:
             ParticipantsManagement().update(
                 room_name=room_name,
                 identity=participant_identity,
-                attributes={"room_admin": "true" if is_admin else "false"},
+                attributes={"room_role": role},
             )
         except ParticipantNotFoundException:
             # The participant left between the presence check and the update: