refactor(ui): rename /api route to /providers

- avoid confusion with backend /api/* endpoints

- update route definition, sidebar nav, and home page link

ui/src/App.tsx

@@ -41,7 +41,7 @@ export default function App() {
               <Route element={<Layout />}>
                 <Route path="/" element={<HomePage />} />
                 <Route path="/analytics" element={<AnalyticsPage />} />
-                <Route path="/api" element={<ApiPage />} />
+                <Route path="/providers" element={<ApiPage />} />
                 <Route path="/cliproxy" element={<CliproxyPage />} />
                 <Route path="/cliproxy/control-panel" element={<CliproxyControlPanelPage />} />
                 <Route path="/copilot" element={<CopilotPage />} />

ui/src/components/layout/app-sidebar.tsx

@@ -44,7 +44,7 @@ const navGroups = [
   {
     title: 'Identity & Access',
     items: [
-      { path: '/api', icon: Key, label: 'API Profiles' },
+      { path: '/providers', icon: Key, label: 'API Profiles' },
       {
         path: '/cliproxy',
         icon: Zap,

ui/src/pages/home.tsx

@@ -138,7 +138,7 @@ export function HomePage() {
               value={overview?.profiles ?? 0}
               icon={Key}
               variant="accent"
-              onClick={() => navigate('/api')}
+              onClick={() => navigate('/providers')}
             />
             <InlineStat
               title="CLIProxy"