feat: complete auction menu parity

app/gateway-frontend/e2e/server-operations.spec.ts

@@ -38,6 +38,7 @@ const profile = (runtimeRunning: boolean) => ({
         profileName: 'che:2',
         apiRunning: runtimeRunning,
         daemonRunning: runtimeRunning,
+        auctionRunning: runtimeRunning,
         tournamentRunning: runtimeRunning,
     },
 });
@@ -212,7 +213,7 @@ test('separates branch and commit semantics and submits a reset from the dedicat
     await page.screenshot({ path: testInfo.outputPath('mobile-operations.png'), fullPage: true });
 });
 
-test('starts and stops both runtime roles through the operation controls', async ({ page }) => {
+test('starts and stops all runtime roles through the operation controls', async ({ page }) => {
     const state: FixtureState = { operations: [], runtimeRunning: false, requestBodies: [] };
     await installFixture(page, state);
     page.on('dialog', (dialog) => dialog.accept());

app/gateway-frontend/src/views/AdminView.vue

@@ -70,6 +70,7 @@ type AdminProfile = {
     runtime: {
         apiRunning: boolean;
         daemonRunning: boolean;
+        auctionRunning: boolean;
         tournamentRunning: boolean;
     };
     buildCommitSha?: string;
@@ -1352,7 +1353,8 @@ onMounted(() => {
                                 </div>
                                 <div class="text-xs text-zinc-400">
                                     상태: {{ profile.status }} / API: {{ profile.runtime.apiRunning ? 'ON' : 'OFF' }} /
-                                    DAEMON: {{ profile.runtime.daemonRunning ? 'ON' : 'OFF' }} / TOURNAMENT:
+                                    DAEMON: {{ profile.runtime.daemonRunning ? 'ON' : 'OFF' }} / AUCTION:
+                                    {{ profile.runtime.auctionRunning ? 'ON' : 'OFF' }} / TOURNAMENT:
                                     {{ profile.runtime.tournamentRunning ? 'ON' : 'OFF' }}
                                 </div>
                             </div>

app/gateway-frontend/src/views/ServerOperationsView.vue

@@ -16,7 +16,12 @@ type Profile = {
     buildWorkspace?: string;
     buildError?: string;
     lastError?: string;
-    runtime: { apiRunning: boolean; daemonRunning: boolean; tournamentRunning: boolean };
+    runtime: {
+        apiRunning: boolean;
+        daemonRunning: boolean;
+        auctionRunning: boolean;
+        tournamentRunning: boolean;
+    };
 };
 
 type Scenario = {
@@ -377,6 +382,12 @@ onBeforeUnmount(() => {
                                 {{ selectedProfile.runtime.daemonRunning ? 'RUNNING' : 'STOPPED' }}
                             </div>
                         </div>
+                        <div class="rounded bg-zinc-950 p-3">
+                            <div class="text-xs text-zinc-500">Auction worker</div>
+                            <div :class="selectedProfile.runtime.auctionRunning ? 'text-emerald-400' : 'text-zinc-500'">
+                                {{ selectedProfile.runtime.auctionRunning ? 'RUNNING' : 'STOPPED' }}
+                            </div>
+                        </div>
                         <div class="rounded bg-zinc-950 p-3">
                             <div class="text-xs text-zinc-500">Tournament worker</div>
                             <div