🧭 fix: Add Base Path Support for Login/Register and Image Paths (#10116)

* fix: add basePath pattern to support login/register and image paths

* Fix linter errors

* refactor: Update import statements for getBasePath and isEnabled, and add path utility functions with tests

- Refactored imports in addImages.js and StableDiffusion.js to use getBasePath from '@librechat/api'.
- Consolidated isEnabled and getBasePath imports in validateImageRequest.js.
- Introduced new path utility functions in path.ts and corresponding unit tests in path.spec.ts to validate base path extraction logic.

* fix: Update domain server base URL in MarkdownComponents and refactor authentication redirection logic

- Changed the domain server base URL in MarkdownComponents.tsx to use the API base URL.
- Refactored the useAuthRedirect hook to utilize React Router's navigate for redirection instead of window.location, ensuring a smoother SPA experience.
- Added unit tests for the useAuthRedirect hook to verify authentication redirection behavior.

* test: Mock isEnabled in validateImages.spec.js for improved test isolation

- Updated validateImages.spec.js to mock the isEnabled function from @librechat/api, ensuring that tests can run independently of the actual implementation.
- Cleared the DOMAIN_CLIENT environment variable before tests to avoid interference with basePath resolution.

---------

Co-authored-by: Danny Avila <danny@librechat.ai>

packages/api/src/utils/path.ts

@@ -0,0 +1,25 @@
+import { logger } from '@librechat/data-schemas';
+
+/**
+ * Gets the base path from the DOMAIN_CLIENT environment variable.
+ * This is useful for constructing URLs when LibreChat is served from a subdirectory.
+ * @returns {string} The base path (e.g., '/librechat' or '')
+ */
+export function getBasePath(): string {
+  if (!process.env.DOMAIN_CLIENT) {
+    return '';
+  }
+
+  try {
+    const clientUrl = new URL(process.env.DOMAIN_CLIENT);
+    // Keep consistent with the logic in api/server/index.js
+    const baseHref = clientUrl.pathname.endsWith('/')
+      ? clientUrl.pathname.slice(0, -1) // Remove trailing slash for path construction
+      : clientUrl.pathname;
+
+    return baseHref === '/' ? '' : baseHref;
+  } catch (error) {
+    logger.warn('Error parsing DOMAIN_CLIENT for base path:', error);
+    return '';
+  }
+}