fix: address Task 2 review findings (stderr + cookie flags)

Co-authored-by: Cursor <cursoragent@cursor.com>

src/lib/bindings/dependencies.ts

@@ -7,12 +7,24 @@ export interface DependencyStatus {
   installCommand: string;
 }
 
+export type CookieSource =
+  | { type: 'browser'; browser: string }
+  | { type: 'file'; path: string }
+  | { type: 'none' };
+
+const DEFAULT_COOKIE_SOURCE: CookieSource = {
+  type: 'browser',
+  browser: 'firefox',
+};
+
 type InstallEvent =
   | { event: 'output'; data: { line: string } }
   | { event: 'finished'; data: { success: boolean } };
 
-export async function checkDependencies(): Promise<DependencyStatus[]> {
-  return invoke<DependencyStatus[]>('check_dependencies');
+export async function checkDependencies(
+  cookieSource: CookieSource = DEFAULT_COOKIE_SOURCE
+): Promise<DependencyStatus[]> {
+  return invoke<DependencyStatus[]>('check_dependencies', { cookieSource });
 }
 
 export async function installDependency(