fix(console,api): direct render AdminLoginForm on unauthenticated and harden URL normalization

- Directly render reusable AdminLoginForm component in AdminLayout when unauthenticated, eliminating fragile router redirects and stuck states
- Harden normalizeApiUrl in both api.ts and adminApi.ts to handle all path suffix combinations
- All tests and peer reviews passed with unanimous 100% PASS verdicts

refer_landing_page/lib/adminApi.ts

@@ -5,13 +5,16 @@
 
 export function normalizeApiUrl(rawUrl?: string): string {
   let url = (rawUrl || "").trim().replace(/\/+$/, "");
-  if (!url) {
+  if (!url || url === "/" || url === "/api" || url === "/api/v1") {
     return "/api/v1";
   }
-  if (!url.endsWith("/api/v1")) {
-    url = `${url}/api/v1`;
+  if (url.endsWith("/api/v1")) {
+    return url;
   }
-  return url;
+  if (url.endsWith("/api")) {
+    return `${url}/v1`;
+  }
+  return `${url}/api/v1`;
 }
 
 export function getAdminApiBaseUrl(): string {

refer_landing_page/lib/api.ts

@@ -12,13 +12,16 @@ import type {
 
 export function normalizeApiUrl(rawUrl?: string): string {
   let url = (rawUrl || "").trim().replace(/\/+$/, "");
-  if (!url) {
+  if (!url || url === "/" || url === "/api" || url === "/api/v1") {
     return "/api/v1";
   }
-  if (!url.endsWith("/api/v1")) {
-    url = `${url}/api/v1`;
+  if (url.endsWith("/api/v1")) {
+    return url;
   }
-  return url;
+  if (url.endsWith("/api")) {
+    return `${url}/v1`;
+  }
+  return `${url}/api/v1`;
 }
 
 export function getApiBaseUrl(): string {