feat(sidebar): add per-folder color swatch with picker and neutral conversation rail

- Add `color` column to folder table with migration backfill and hash-based assignment on folder creation
- Expose `update_folder_color` via Tauri command and `/update_folder_color` HTTP route
- Render a color swatch before each folder name in the sidebar header; offer a 10-color palette (9 hues plus a theme-aware foreground sentinel) through the folder context menu
- Show the folder header "new conversation" button only on hover
- Drop the expanded-state tint on folder name and count badge; use a fixed neutral rail color for conversation items

src-tauri/src/db/migration/m20260424_000001_folder_color.rs

@@ -0,0 +1,60 @@
+use sea_orm_migration::prelude::*;
+use sea_orm_migration::sea_orm::{ConnectionTrait, DbBackend, Statement};
+
+#[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)
+                    .add_column(
+                        ColumnDef::new(Folder::Color)
+                            .string()
+                            .not_null()
+                            .default("#22c55e"),
+                    )
+                    .to_owned(),
+            )
+            .await?;
+
+        // Backfill existing rows with a palette color chosen by (id - 1) mod N,
+        // so existing workspaces get visually distinct swatches after migration.
+        let conn = manager.get_connection();
+        let sql = "UPDATE folder SET color = CASE ((id - 1) % 9) \
+            WHEN 0 THEN '#ef4444' \
+            WHEN 1 THEN '#f97316' \
+            WHEN 2 THEN '#eab308' \
+            WHEN 3 THEN '#84cc16' \
+            WHEN 4 THEN '#22c55e' \
+            WHEN 5 THEN '#06b6d4' \
+            WHEN 6 THEN '#8b5cf6' \
+            WHEN 7 THEN '#d946ef' \
+            WHEN 8 THEN '#ec4899' \
+            END";
+        conn.execute(Statement::from_string(DbBackend::Sqlite, sql.to_string()))
+            .await?;
+
+        Ok(())
+    }
+
+    async fn down(&self, manager: &SchemaManager) -> Result<(), DbErr> {
+        manager
+            .alter_table(
+                Table::alter()
+                    .table(Folder::Table)
+                    .drop_column(Folder::Color)
+                    .to_owned(),
+            )
+            .await
+    }
+}
+
+#[derive(DeriveIden)]
+enum Folder {
+    Table,
+    Color,
+}

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

@@ -12,6 +12,7 @@ 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;
+mod m20260424_000001_folder_color;
 pub struct Migrator;
 
 #[async_trait::async_trait]
@@ -30,6 +31,7 @@ impl MigratorTrait for Migrator {
             Box::new(m20260420_000001_opened_tabs::Migration),
             Box::new(m20260422_000001_folder_sort_order::Migration),
             Box::new(m20260423_000001_drop_folder_parent_branch::Migration),
+            Box::new(m20260424_000001_folder_color::Migration),
         ]
     }
 }