Add chat thread forking

server/prisma/schema.prisma

@@ -51,7 +51,8 @@ model Chat {
   createdAt DateTime @default(now())
   updatedAt DateTime @updatedAt
 
-  title String?
+  title                  String?
+  titleGenerationPending Boolean @default(false)
 
   initiatedProvider Provider?
   initiatedModel    String?
@@ -64,11 +65,17 @@ model Chat {
   user   User?   @relation(fields: [userId], references: [id])
   userId String?
 
+  // Forks always point directly to the single root chat, never to another fork.
+  parentChat   Chat?  @relation("ChatForks", fields: [parentChatId], references: [id], onDelete: Cascade)
+  parentChatId String?
+  childChats   Chat[] @relation("ChatForks")
+
   messages Message[]
   calls    LlmCall[]
   projectItems ProjectItem[]
 
   @@index([userId])
+  @@index([parentChatId])
 }
 
 model Message {