fix: preserve custom paths in SSE endpoint URLs

When an SSE client connects with a custom path (e.g., /api/v1/custom/sse),
ensure the endpoint URL maintains the same base path structure but with
/messages instead of /sse. This fixes issues where custom endpoints were
getting collapsed to the root path.

Should fix issues reported in modelcontextprotocol/inspector#313 and #296
Tests demonstrating the issue were added in PR #439

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

src/client/sse.ts

@@ -143,7 +143,18 @@ export class SSEClientTransport implements Transport {
         const messageEvent = event as MessageEvent;
 
         try {
+          // Use the original URL as the base to resolve the received endpoint
           this._endpoint = new URL(messageEvent.data, this._url);
+          
+          // If the original URL had a custom path, preserve it in the endpoint URL
+          const originalPath = this._url.pathname;
+          if (originalPath && originalPath !== '/' && originalPath !== '/sse') {
+            // Extract the base path from the original URL (everything before the /sse suffix)
+            const basePath = originalPath.replace(/\/sse$/, '');
+            // The endpoint should use the same base path but with /messages instead of /sse
+            this._endpoint.pathname = basePath + '/messages';
+          }
+          
           if (this._endpoint.origin !== this._url.origin) {
             throw new Error(
               `Endpoint origin does not match connection origin: ${this._endpoint.origin}`,