refactor(branch-dropdown): drop worktree parent-branch merge shortcut

Remove the parent-branch button shown beside the branch selector along
with its supporting API, command, service, model, and i18n strings.
Add migration m20260423 to drop the now-unused folder.parent_branch
column.

src-tauri/src/db/entities/folder.rs

@@ -15,7 +15,6 @@ pub struct Model {
     pub updated_at: DateTimeUtc,
     pub deleted_at: Option<DateTimeUtc>,
     pub is_open: bool,
-    pub parent_branch: Option<String>,
     pub sort_order: i32,
 }
 

src-tauri/src/db/migration/m20260423_000001_drop_folder_parent_branch.rs

@@ -0,0 +1,35 @@
+use sea_orm_migration::prelude::*;
+
+#[derive(DeriveMigrationName)]
+pub struct Migration;
+
+#[async_trait::async_trait]
+impl MigrationTrait for Migration {
+    async fn up(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .alter_table(
+                Table::alter()
+                    .table(Folder::Table)
+                    .drop_column(Folder::ParentBranch)
+                    .to_owned(),
+            )
+            .await
+    }
+
+    async fn down(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .alter_table(
+                Table::alter()
+                    .table(Folder::Table)
+                    .add_column(ColumnDef::new(Folder::ParentBranch).string().null())
+                    .to_owned(),
+            )
+            .await
+    }
+}
+
+#[derive(DeriveIden)]
+enum Folder {
+    Table,
+    ParentBranch,
+}

src-tauri/src/db/migration/mod.rs

@@ -11,6 +11,7 @@ mod m20260404_000001_model_provider;
 mod m20260406_000001_agent_setting_model_provider;
 mod m20260420_000001_opened_tabs;
 mod m20260422_000001_folder_sort_order;
+mod m20260423_000001_drop_folder_parent_branch;
 pub struct Migrator;
 
 #[async_trait::async_trait]
@@ -28,6 +29,7 @@ impl MigratorTrait for Migrator {
             Box::new(m20260406_000001_agent_setting_model_provider::Migration),
             Box::new(m20260420_000001_opened_tabs::Migration),
             Box::new(m20260422_000001_folder_sort_order::Migration),
+            Box::new(m20260423_000001_drop_folder_parent_branch::Migration),
         ]
     }
 }

src-tauri/src/db/service/folder_service.rs

@@ -31,7 +31,6 @@ fn to_detail(m: folder::Model) -> FolderDetail {
         name: m.name,
         path: m.path,
         git_branch: m.git_branch,
-        parent_branch: m.parent_branch,
         default_agent_type,
         last_opened_at: m.last_opened_at,
         sort_order: m.sort_order,
@@ -85,7 +84,6 @@ pub async fn add_folder(
             name: Set(name),
             path: Set(path.to_string()),
             git_branch: Set(None),
-            parent_branch: Set(None),
             default_agent_type: Set(None),
             last_opened_at: Set(now),
             created_at: Set(now),
@@ -127,22 +125,6 @@ pub async fn remove_folder(conn: &DatabaseConnection, path: &str) -> Result<(),
     Ok(())
 }
 
-pub async fn set_folder_parent_branch(
-    conn: &DatabaseConnection,
-    folder_id: i32,
-    parent_branch: Option<String>,
-) -> Result<(), DbError> {
-    let row = folder::Entity::find_by_id(folder_id).one(conn).await?;
-
-    if let Some(row) = row {
-        let mut active = row.into_active_model();
-        active.parent_branch = Set(parent_branch);
-        active.updated_at = Set(Utc::now());
-        active.update(conn).await?;
-    }
-    Ok(())
-}
-
 pub async fn set_folder_open(
     conn: &DatabaseConnection,
     folder_id: i32,