feat(providers): add Kimchi API key support (dual OAuth + API key)

Kimchi's transport is OpenAI-compatible (Authorization: Bearer) but the
registry declared it OAuth-only, so the dashboard, /api/providers, and
the connection test all rejected API keys. Enable dual auth
(authModes: ["oauth", "apikey"]) and add a kimchi case to
testApiKeyConnection so the Test Connection button works for both modes.
Regenerate the golden snapshot with the Kimchi entries (+ other
previously-missing providers).

src/app/api/providers/[id]/test/testUtils.js

@@ -788,13 +788,27 @@ async function testApiKeyConnection(connection, effectiveProxy = null) {
         );
         return { valid: exRes.ok, error: exRes.ok ? null : "Invalid Personal Access Token" };
       }
-      case "llm7": {
+case "llm7": {
         const baseUrl = connection.providerSpecificData?.baseUrl || "https://api.llm7.io/v1";
         const res = await fetchWithConnectionProxy(`${baseUrl.replace(/\/$/, "")}/models`, {
           headers: { Authorization: `Bearer ${connection.apiKey}` },
         }, effectiveProxy);
         return { valid: res.ok, error: res.ok ? null : "Invalid API key or base URL" };
       }
+      case "kimchi": {
+        // Dual-auth: same validation endpoint as the OAuth flow — the token (API key
+        // or OAuth access token) is sent as Authorization: Bearer.
+        const url = KIMCHI_CONFIG.validationUrl || "https://api.cast.ai/v1/llm/openai/supported-providers";
+        const res = await fetchWithConnectionProxy(url, {
+          method: "GET",
+          headers: {
+            Accept: "application/json",
+            Authorization: `Bearer ${connection.apiKey}`,
+            "User-Agent": "kimchi/0.1.40",
+          },
+        }, effectiveProxy);
+        return { valid: res.ok, error: res.ok ? null : "Invalid API key", refreshed: false };
+      }
       default:
         return { valid: false, error: "Provider test not supported" };
     }