Expose `schema_generator` on `FastMCP` for tool params schema generation

Description

Context

Tool.from_function (in src/mcp/server/fastmcp/tools/base.py) generates the
tool parameters JSON schema via:

parameters = func_arg_metadata.arg_model.model_json_schema(by_alias=True)

This is hardcoded — no way for users to customize the generation. Pydantic 2.11+
supports union_format='primitive_type_array' which produces compact
LLM-friendly schemas like {"type": ["integer", "string"]} instead of
{"anyOf": [...]}. There's no path to enable it without monkey-patching or
post-processing.

Proposal

Add schema_generator: type[GenerateJsonSchema] | None = None to FastMCP.__init__.
When provided, plumb it to both model_json_schema calls:

# tools/base.py
parameters = func_arg_metadata.arg_model.model_json_schema(
    by_alias=True,
    schema_generator=self.schema_generator or GenerateJsonSchema,
)

# utilities/func_metadata.py
schema = model.model_json_schema(
    schema_generator=self.schema_generator or StrictJsonSchema,
)

Use case

from pydantic.json_schema import GenerateJsonSchema

class CompactUnionGen(GenerateJsonSchema):
    def __init__(self, by_alias=True, ref_template='#/$defs/{model}'):
        super().__init__(
            by_alias=by_alias,
            ref_template=ref_template,
            union_format='primitive_type_array',
        )

mcp = FastMCP("srv", schema_generator=CompactUnionGen)

Tradeoff to discuss

func_metadata.py currently uses StrictJsonSchema (warnings → errors). With a
user-supplied generator, strict semantics are lost unless the user extends
StrictJsonSchema themselves. Proposed resolution: document that custom
generators should extend StrictJsonSchema if strict output validation is
desired.

Backward compat

Default None preserves current behavior exactly.

References

No response

Commencez par src/mcp/server/fastmcp/tools/base.py et utilities/func_metadata.py, puis retracez comment les valeurs de FastMCP.init parviennent aux deux appels à model_json_schema. La modification est terminée lorsqu’un schema_generator optionnel atteint les deux chemins, que les valeurs par défaut préservent le comportement actuel et que le compromis lié à strict-schema est documenté ou couvert comme proposé.