Null fields in JsonSchema without @Nullable annotation break serialization with Jackson

Bug description
When connecting as a client to an MCP server written with fastmcp 2.12.3, some tool input schemas received from the server are deserialized in Java with a number of JsonSchema fields set to null: required, additionalProperties, defs, and definitions.

This breaks Jackson serialization for the resulting JsonSchema:

McpSyncClient client = ...;
Tool tool = client.listTools().tools().get(0);
tool.inputSchema().required()  // -> null
tool.inputSchema().additionalProperties()  // -> null
tool.inputSchema().defs()  // -> null
tool.inputSchema().definitions()  // -> null
(new ObjectMapper()).valueToTree(tool.inputSchema)

Results in:

java.lang.IllegalArgumentException: Non-nullable field additionalProperties was null, annotate with @Nullable if this is expected (through reference chain: io.modelcontextprotocol.spec.McpSchema$JsonSchema["additionalProperties"])

As a workaround, you can reconstruct the JsonSchema with some sensible defaults before serializing:

new JsonSchema(inputSchema.type, inputSchema.properties, List.of(), true, Map.of(), Map.of())

which resolves the issue.

Environment

• Observed on a Mac, library version 0.13.1, Java 21

Steps to reproduce
See above.

Expected behavior
Jackson should be able to serialize JsonSchema objects provided by the client.

Either:

• JsonSchema should have default values for these fields instead of defaulting to null, OR
• These fields should be annotated with @Nullable

Minimal Complete Reproducible example
It's difficult without also providing an example of the server, but let me know if anything is unclear or if I can provide any additional details.

Comienza con el modelo JsonSchema expuesto a través de tool.inputSchema y reproduce la serialización con ObjectMapper usando los campos mencionados en el informe. Determina si los campos afectados deben recibir valores predeterminados o marcarse como nullable y, después, verifica que un JsonSchema proporcionado por el cliente pueda serializarse sin la excepción indicada.