fix: fall back to SSE transport when Streamable HTTP probe fails

Many MCP servers only support legacy SSE despite being configured as
generic HTTP endpoints. Follow the MCP SDK's recommended fallback
pattern: try Streamable HTTP first, then retry with SSE on failure.
This matches VS Code's behavior for these servers.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

src/main/services/mcpToolProber.ts

@@ -89,7 +89,29 @@ async function probeServerCore(
   server: McpServerDefinition,
   tokenLookup?: (serverUrl: string) => string | undefined,
 ): Promise<McpProbedTool[]> {
-  const transport = createTransport(server, tokenLookup);
+  if (server.transport === 'local' || server.transport === 'sse') {
+    return probeWithTransport(createTransport(server, tokenLookup));
+  }
+
+  // For HTTP servers, try Streamable HTTP first, then fall back to SSE.
+  // Many MCP servers only support SSE despite being configured as generic HTTP.
+  const headers = buildHeaders(server.url, server.headers, tokenLookup);
+  const headerOpts = headers ? { requestInit: { headers } } : undefined;
+
+  try {
+    return await probeWithTransport(
+      new StreamableHTTPClientTransport(new URL(server.url), headerOpts),
+    );
+  } catch {
+    return probeWithTransport(
+      new SSEClientTransport(new URL(server.url), headerOpts),
+    );
+  }
+}
+
+async function probeWithTransport(
+  transport: InstanceType<typeof StdioClientTransport> | InstanceType<typeof SSEClientTransport> | InstanceType<typeof StreamableHTTPClientTransport>,
+): Promise<McpProbedTool[]> {
   const client = new Client(CLIENT_INFO, { capabilities: {} });
 
   try {
@@ -133,15 +155,7 @@ function createTransport(
   }
 
   const headers = buildHeaders(server.url, server.headers, tokenLookup);
-
-  if (server.transport === 'sse') {
-    return new SSEClientTransport(
-      new URL(server.url),
-      headers ? { requestInit: { headers } } : undefined,
-    );
-  }
-
-  return new StreamableHTTPClientTransport(
+  return new SSEClientTransport(
     new URL(server.url),
     headers ? { requestInit: { headers } } : undefined,
   );