fix: add EXA_API_KEY header support for websearch_exa MCP (#499)

The remote MCP endpoint https://mcp.exa.ai/mcp requires API key authentication
via x-api-key header. Without this, the connection times out waiting for auth.

This change:
- Reads EXA_API_KEY from environment variable
- Passes it as x-api-key header when available
- Updates RemoteMcpConfig type to support optional headers

Co-authored-by: Junho Yeo <i@junho.io>

src/mcp/index.ts

@@ -5,14 +5,21 @@ import type { McpName } from "./types"
 
 export { McpNameSchema, type McpName } from "./types"
 
-const allBuiltinMcps: Record<McpName, { type: "remote"; url: string; enabled: boolean }> = {
+type RemoteMcpConfig = {
+  type: "remote"
+  url: string
+  enabled: boolean
+  headers?: Record<string, string>
+}
+
+const allBuiltinMcps: Record<McpName, RemoteMcpConfig> = {
   websearch,
   context7,
   grep_app,
 }
 
 export function createBuiltinMcps(disabledMcps: string[] = []) {
-  const mcps: Record<string, { type: "remote"; url: string; enabled: boolean }> = {}
+  const mcps: Record<string, RemoteMcpConfig> = {}
 
   for (const [name, config] of Object.entries(allBuiltinMcps)) {
     if (!disabledMcps.includes(name)) {

src/mcp/websearch.ts

@@ -2,4 +2,7 @@ export const websearch = {
   type: "remote" as const,
   url: "https://mcp.exa.ai/mcp?tools=web_search_exa",
   enabled: true,
+  headers: process.env.EXA_API_KEY
+    ? { "x-api-key": process.env.EXA_API_KEY }
+    : undefined,
 }