Tool input schema does not include $schema property

[vivekschauhan]

Bug description

Based on specification Tool input schema follows the JSON schema usage guideline(https://modelcontextprotocol.io/specification/2025-11-25/basic#schema-dialect) that states the use of $schema field to specify explicit dialect and defaults to JSON Schema 2020-12 if the field is not present, however JsonSchema record used for defining inputSchema property in Tool does not include $schema property.

This causes the $schema property not to be included in the serialized response for tool/list request and may causes ambiguity for MCP clients when interpreting which schema version to use.

Steps to reproduce
Diff with test included in java-sdk/mcp-core/src/test/java/io/modelcontextprotocol/spec/McpSchemaTests.java

diff --git a/mcp-core/src/test/java/io/modelcontextprotocol/spec/McpSchemaTests.java b/mcp-core/src/test/java/io/modelcontextprotocol/spec/McpSchemaTests.java
index 82ffe9e..c943a40 100644
--- a/mcp-core/src/test/java/io/modelcontextprotocol/spec/McpSchemaTests.java
+++ b/mcp-core/src/test/java/io/modelcontextprotocol/spec/McpSchemaTests.java
@@ -920,6 +920,53 @@ public class McpSchemaTests {
 					"""));
 	}
 
+	@Test
+	void testToolWithVersionedInputSchema() throws Exception {
+		String inputSchemaJson = """
+				{
+					"$schema": "https://json-schema.org/draft-07/schema#",
+					"type": "object",
+					"properties": {
+						"name": {
+							"type": "string"
+						},
+						"value": {
+							"type": "number"
+						}
+					},
+					"required": ["name"],
+					"additionalProperties": false
+				}
+				""";
+
+		McpSchema.Tool tool = McpSchema.Tool.builder()
+				.name("test-tool")
+				.description("A test tool")
+				.inputSchema(JSON_MAPPER, inputSchemaJson)
+				.build();
+
+		String value = JSON_MAPPER.writeValueAsString(tool);
+		assertThatJson(value).when(Option.IGNORING_ARRAY_ORDER)
+				.when(Option.IGNORING_EXTRA_ARRAY_ITEMS)
+				.isObject()
+				.isEqualTo(json("""
+					{
+						"name":"test-tool",
+						"description":"A test tool",
+						"inputSchema":{
+							"$schema":"https://json-schema.org/draft-07/schema#",
+							"type":"object",
+							"properties":{
+								"name":{"type":"string"},
+								"value":{"type":"number"}
+							},
+							"required":["name"],
+							"additionalProperties": false
+						}
+					}
+					"""));
+	}
+
 	@Test
 	void testToolWithOutputSchema() throws Exception {
 		String inputSchemaJson = """

Expected behavior
$schema property included in tool inputSchema if implementation uses explicit JSON schema dialect