Fix extensions field to use JSONObjectSchema instead of removed AssertObjectSchema

The merge with main brought in modelcontextprotocol#1612 which replaced AssertObjectSchema
with JSONObjectSchema, but the extensions fields were not updated.
Also fixes spec.types.ts to use JSONObject (matching experimental)
for bidirectional type compatibility.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: chughtapan

packages/core/src/types/spec.types.ts

@@ -586,7 +586,7 @@ export interface ClientCapabilities {
      * @example Extensions — UI extension with MIME type support
      * {@includeCode ./examples/ClientCapabilities/extensions-ui-mime-types.json}
      */
-    extensions?: { [key: string]: object };
+    extensions?: { [key: string]: JSONObject };
 }
 
 /**
@@ -703,7 +703,7 @@ export interface ServerCapabilities {
      * @example Extensions — UI extension support
      * {@includeCode ./examples/ServerCapabilities/extensions-ui.json}
      */
-    extensions?: { [key: string]: object };
+    extensions?: { [key: string]: JSONObject };
 }
 
 /**

packages/core/src/types/types.ts

@@ -560,7 +560,7 @@ export const ClientCapabilitiesSchema = z.object({
     /**
      * Extensions that the client supports. Keys are extension identifiers (vendor-prefix/extension-name).
      */
-    extensions: z.record(z.string(), AssertObjectSchema).optional()
+    extensions: z.record(z.string(), JSONObjectSchema).optional()
 });
 
 export const InitializeRequestParamsSchema = BaseRequestParamsSchema.extend({
@@ -642,7 +642,7 @@ export const ServerCapabilitiesSchema = z.object({
     /**
      * Extensions that the server supports. Keys are extension identifiers (vendor-prefix/extension-name).
      */
-    extensions: z.record(z.string(), AssertObjectSchema).optional()
+    extensions: z.record(z.string(), JSONObjectSchema).optional()
 });
 
 /**