Nested structs not correctly flattened in JSON schema

[unbekanntes-pferd]

Describe the bug
Nested structs not correctly flattened for JSON schema:
See code example below - in short: having a nested struct produces the correct JSON string but incorrect JSON schema via tool registration.

To Reproduce
Steps to reproduce the behavior:

package main

import (
	"context"
	"log"
	"github.com/modelcontextprotocol/go-sdk/mcp"
)

// Foo represents a base struct
type Foo struct {
	ID   string `json:"id"`
	Name string `json:"name"`
	Type string `json:"type"`
}

// Bar embeds Foo
type Bar struct {
	*Foo                        // Embedded - should flatten in JSON
	Extra string `json:"extra"` // Additional field
}

// Response contains array of embedded structs
type Response struct {
	Data []Bar `json:"data"`
}

// Input for the tool
type Input struct {
	Count int `json:"count"`
}

// TestTool demonstrates the embedded struct schema bug
func TestTool(ctx context.Context, req *mcp.CallToolRequest, input Input) (*mcp.CallToolResult, Response, error) {
	// Create test data with embedded structs
	response := Response{
		Data: []Bar{
			{
				Foo: &Foo{
					ID:   "foo1",
					Name: "Test Foo 1",
					Type: "test",
				},
				Extra: "additional data 1",
			},
			{
				Foo: &Foo{
					ID:   "foo2", 
					Name: "Test Foo 2",
					Type: "test",
				},
				Extra: "additional data 2",
			},
		},
	}

	return nil, response, nil
}

func main() {
	ctx := context.Background()
	clientTransport, serverTransport := mcp.NewInMemoryTransports()

	server := mcp.NewServer(&mcp.Implementation{Name: "bug-repro", Version: "v0.0.1"}, nil)
	
	// This should work but will fail with schema validation error
	// because SDK expects {"Foo": {...}, "extra": "..."} 
	// but Go produces {"id": "...", "name": "...", "type": "...", "extra": "..."}
	mcp.AddTool(server, &mcp.Tool{
		Name:        "test_embedded_struct",
		Description: "Test tool that demonstrates embedded struct schema bug",
	}, TestTool)

	serverSession, err := server.Connect(ctx, serverTransport, nil)
	if err != nil {
		log.Fatal(err)
	}

	client := mcp.NewClient(&mcp.Implementation{Name: "client"}, nil)
	clientSession, err := client.Connect(ctx, clientTransport, nil)
	if err != nil {
		log.Fatal(err)
	}

	// This call will fail with schema validation error
	res, err := clientSession.CallTool(ctx, &mcp.CallToolParams{
		Name:      "test_embedded_struct",
		Arguments: map[string]any{"count": 2},
	})
	if err != nil {
		log.Printf("ERROR (demonstrates the bug): %v", err)
	} else {
		log.Printf("Success: %+v", res)
	}

	clientSession.Close()
	serverSession.Wait()
}

Expected behavior
Embedded structs are flattened (as with JSON string) in JSON schema.

Logs
Output of above:

2025/09/09 16:51:15 ERROR (demonstrates the bug): calling "tools/call": tool output: validating
        &{[{0x14000282660 additional data 1} {0x14000282690 additional data 2}]}
against
         {"type":"object","required":["data"],"properties":{"data":{"type":"array","items":{"type":"object","required":["Foo","extra"],"properties":{"Foo":{"type":["null","object"],"required":["id","name","type"],"properties":{"id":{"type":"string"},"name":{"type":"string"},"type":{"type":"string"}},"additionalProperties":false},"extra":{"type":"string"}},"additionalProperties":false}}},"additionalProperties":false}:
 validating root: validating /properties/data: validating /properties/data/items: validating /properties/data/items/additionalProperties: not: validated against <anonymous schema>

Additional context
N/A

[findleyr]

Thank you.

As a temporary workaround, you can provide the schema explicitly.
However, we will fix this upstream and update the jsonschema package.

[findleyr]

This is really a bug in jsonschema-go, but let's leave this issue open for visibility.