feat(kimchi): add Kimchi OAuth provider support

Add Kimchi as a browser-token OAuth provider routed through its
OpenAI-compatible gateway. Discover live models for /v1/models and
provider models, normalize Claude-compatible requests, and wire up
provider connection tests.

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

src/app/api/oauth/[provider]/[action]/route.js

@@ -232,8 +232,8 @@ export async function POST(request, { params }) {
         });
       }
 
-      // Cline uses authorization_code without PKCE
-      const noPkceExchangeProviders = ["cline"];
+      // Cline uses authorization_code without PKCE. Kimchi returns a browser token.
+      const noPkceExchangeProviders = ["cline", "kimchi"];
       if (!code || !redirectUri || (!codeVerifier && !noPkceExchangeProviders.includes(provider))) {
         return NextResponse.json({ error: "Missing required fields" }, { status: 400 });
       }