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/web/handlers/folders.rs

@@ -140,6 +140,25 @@ pub async fn reorder_folders(
     Ok(Json(()))
 }
 
+#[derive(Deserialize)]
+#[serde(rename_all = "camelCase")]
+pub struct UpdateFolderColorParams {
+    pub folder_id: i32,
+    pub color: String,
+}
+
+pub async fn update_folder_color(
+    Extension(state): Extension<Arc<AppState>>,
+    Json(params): Json<UpdateFolderColorParams>,
+) -> Result<Json<FolderDetail>, AppCommandError> {
+    let db = &state.db;
+    let folder = folder_service::update_folder_color(&db.conn, params.folder_id, &params.color)
+        .await
+        .map_err(AppCommandError::from)?
+        .ok_or_else(|| AppCommandError::not_found("Folder not found"))?;
+    Ok(Json(folder))
+}
+
 #[derive(Deserialize)]
 #[serde(rename_all = "camelCase")]
 pub struct PathParams {

src-tauri/src/web/router.rs

@@ -107,6 +107,10 @@ pub fn build_router(state: Arc<AppState>, token: String, static_dir: std::path::
             post(handlers::folders::remove_folder_from_workspace),
         )
         .route("/reorder_folders", post(handlers::folders::reorder_folders))
+        .route(
+            "/update_folder_color",
+            post(handlers::folders::update_folder_color),
+        )
         .route(
             "/add_folder_to_history",
             post(handlers::folders::add_folder_to_history),