Refactor SSEClientTransport to cache wrapped fetch function

Match the pattern used in StreamableHTTPClientTransport by creating
the wrapped fetch function once in the constructor instead of
recreating it on every auth call. This improves consistency between
the two transport implementations and avoids unnecessary function
recreation.

Changes:
- Add _fetchWithInit field to store the wrapped fetch function
- Initialize _fetchWithInit in constructor using createFetchWithInit
- Use _fetchWithInit in all auth() calls instead of creating inline
- Remove redundant createFetchWithInit calls from 3 locations

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

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

Author: dsp-ant

src/client/sse.ts

@@ -70,6 +70,7 @@ export class SSEClientTransport implements Transport {
     private _requestInit?: RequestInit;
     private _authProvider?: OAuthClientProvider;
     private _fetch?: FetchLike;
+    private _fetchWithInit: FetchLike;
     private _protocolVersion?: string;
 
     onclose?: () => void;
@@ -84,6 +85,7 @@ export class SSEClientTransport implements Transport {
         this._requestInit = opts?.requestInit;
         this._authProvider = opts?.authProvider;
         this._fetch = opts?.fetch;
+        this._fetchWithInit = createFetchWithInit(opts?.fetch, opts?.requestInit);
     }
 
     private async _authThenStart(): Promise<void> {
@@ -93,14 +95,11 @@ export class SSEClientTransport implements Transport {
 
         let result: AuthResult;
         try {
-            // Wrap fetch to automatically include base RequestInit options
-            const fetchFn = createFetchWithInit(this._fetch, this._requestInit);
-
             result = await auth(this._authProvider, {
                 serverUrl: this._url,
                 resourceMetadataUrl: this._resourceMetadataUrl,
                 scope: this._scope,
-                fetchFn
+                fetchFn: this._fetchWithInit
             });
         } catch (error) {
             this.onerror?.(error as Error);
@@ -218,15 +217,12 @@ export class SSEClientTransport implements Transport {
             throw new UnauthorizedError('No auth provider');
         }
 
-        // Wrap fetch to automatically include base RequestInit options
-        const fetchFn = createFetchWithInit(this._fetch, this._requestInit);
-
         const result = await auth(this._authProvider, {
             serverUrl: this._url,
             authorizationCode,
             resourceMetadataUrl: this._resourceMetadataUrl,
             scope: this._scope,
-            fetchFn
+            fetchFn: this._fetchWithInit
         });
         if (result !== 'AUTHORIZED') {
             throw new UnauthorizedError('Failed to authorize');
@@ -262,14 +258,11 @@ export class SSEClientTransport implements Transport {
                     this._resourceMetadataUrl = resourceMetadataUrl;
                     this._scope = scope;
 
-                    // Wrap fetch to automatically include base RequestInit options
-                    const fetchFn = createFetchWithInit(this._fetch, this._requestInit);
-
                     const result = await auth(this._authProvider, {
                         serverUrl: this._url,
                         resourceMetadataUrl: this._resourceMetadataUrl,
                         scope: this._scope,
-                        fetchFn
+                        fetchFn: this._fetchWithInit
                     });
                     if (result !== 'AUTHORIZED') {
                         throw new UnauthorizedError();