fix: remove workdir management kind

crates/worker-runtime/src/catalog.rs

@@ -156,10 +156,6 @@ pub struct WorkingDirectorySummary {
     pub cleanliness: Option<String>,
     #[serde(default, skip_serializing_if = "Option::is_none")]
     pub primary_worker_id: Option<WorkerId>,
-    /// Backend projection metadata. Runtimes leave this absent; Workspace Browser
-    /// APIs fill it with `backend_managed` or `runtime_unmanaged`.
-    #[serde(default, skip_serializing_if = "Option::is_none")]
-    pub management_kind: Option<String>,
 }
 
 #[derive(Clone, Debug, PartialEq, Eq, Serialize, Deserialize)]

crates/worker-runtime/src/working_directory.rs

@@ -48,7 +48,6 @@ impl WorkingDirectory {
             status: self.status.clone(),
             cleanliness: None,
             primary_worker_id: None,
-            management_kind: None,
         }
     }
 }
@@ -222,7 +221,6 @@ impl LocalGitWorktreeMaterializer {
                 status: WorkingDirectoryStatusKind::Corrupted,
                 cleanliness: Some("unknown".to_string()),
                 primary_worker_id: None,
-                management_kind: None,
             },
         }
     }