feat: Gemini image generation test button in admin settings

API: new testGeminiConnection adminProcedure
- Generates a simple test image via Gemini API
- Returns { ok, model } on success, { ok: false, error } on failure
- Audit logged: "Gemini test succeeded/failed"

UI: "Test Gemini" button next to "Save Image Settings"
- Only visible when Gemini provider is selected
- Shows green success or red error result below the buttons
- Displays the model name on success

Model: gemini-2.0-flash-preview-image-generation (correct name)

Co-Authored-By: claude-flow <ruv@ruv.net>

apps/web/src/components/admin/SystemSettingsClient.tsx

@@ -257,6 +257,12 @@ export function SystemSettingsClient() {
     },
   });
 
+  const [geminiTestResult, setGeminiTestResult] = useState<{ ok: boolean; model?: string; error?: string } | null>(null);
+  const testGeminiMut = trpc.settings.testGeminiConnection.useMutation({
+    onSuccess: (data) => setGeminiTestResult(data as any),
+    onError: (err) => setGeminiTestResult({ ok: false, error: err.message }),
+  });
+
   function handleSaveSmtp() {
     saveSmtpMutation.mutate({
       smtpHost: smtpHost || undefined,
@@ -1187,7 +1193,7 @@ export function SystemSettingsClient() {
           </div>
         )}
 
-        <div className="flex items-center gap-3 pt-1">
+        <div className="flex flex-wrap items-center gap-3 pt-1">
           <button
             type="button"
             className={PRIMARY_BUTTON_CLASS}
@@ -1196,10 +1202,31 @@ export function SystemSettingsClient() {
           >
             {saveImageMutation.isPending ? "Saving..." : "Save Image Settings"}
           </button>
+          {imageProvider === "gemini" && (
+            <button
+              type="button"
+              className="px-4 py-2 border border-gray-300 dark:border-gray-600 text-gray-700 dark:text-gray-200 rounded-lg hover:bg-gray-50 dark:hover:bg-gray-700 text-sm font-medium disabled:opacity-50"
+              disabled={testGeminiMut.isPending}
+              onClick={() => testGeminiMut.mutate()}
+            >
+              {testGeminiMut.isPending ? "Testing..." : "Test Gemini"}
+            </button>
+          )}
           {imageSaved && (
             <span className="text-sm font-medium text-green-600 dark:text-green-400">Saved</span>
           )}
         </div>
+        {geminiTestResult && (
+          <div className={`mt-3 rounded-lg px-3 py-2 text-sm ${
+            geminiTestResult.ok
+              ? "bg-green-50 text-green-700 border border-green-200 dark:bg-green-900/20 dark:text-green-300 dark:border-green-800"
+              : "bg-red-50 text-red-700 border border-red-200 dark:bg-red-900/20 dark:text-red-300 dark:border-red-800"
+          }`}>
+            {geminiTestResult.ok
+              ? `Gemini image generation works! Model: ${(geminiTestResult as any).model}`
+              : `Test failed: ${(geminiTestResult as any).error}`}
+          </div>
+        )}
       </div>
 
       {/* ── SMTP / Email ──────────────────────────────────────────── */}