refactor: extract OAuth helper functions and simplify provider state

src/mcp/client/auth/__init__.py

@@ -4,11 +4,9 @@
 Implements authorization code flow with PKCE and automatic token refresh.
 """
 
+from mcp.client.auth.exceptions import OAuthFlowError, OAuthRegistrationError, OAuthTokenError
 from mcp.client.auth.oauth2 import (
     OAuthClientProvider,
-    OAuthFlowError,
-    OAuthRegistrationError,
-    OAuthTokenError,
     PKCEParameters,
     TokenStorage,
 )

src/mcp/client/auth/exceptions.py

@@ -0,0 +1,10 @@
+class OAuthFlowError(Exception):
+    """Base exception for OAuth flow errors."""
+
+
+class OAuthTokenError(OAuthFlowError):
+    """Raised when token operations fail."""
+
+
+class OAuthRegistrationError(OAuthFlowError):
+    """Raised when client registration fails."""