fix: align ForkInfo type with backend schema, remove redundant fork fields

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/src/types/tree.ts

@@ -140,10 +140,11 @@ export interface ProceduralTreeStructure {
 }
 
 export interface ForkInfo {
-  parent_tree_id: string
-  parent_tree_name: string | null
-  fork_depth: number
+  parent_tree_id: string | null
+  root_tree_id: string | null
   fork_reason: string | null
+  fork_depth: number
+  parent_updated_at: string | null
   has_parent_updates: boolean
 }
 
@@ -173,8 +174,6 @@ export interface Tree {
   updated_at: string
   usage_count: number
   fork_info?: ForkInfo | null
-  parent_tree_id?: string | null
-  fork_depth?: number
 }
 
 export interface TreeListItem {
@@ -198,8 +197,6 @@ export interface TreeListItem {
   created_at: string
   updated_at: string
   visibility: 'private' | 'team' | 'link' | 'public'
-  fork_depth?: number
-  parent_tree_id?: string | null
 }
 
 export interface TreeCreate {