Infer execute input from inputSchema - #6

Infer callback inputs at the registerTool boundary so inputSchema remains the single source of truth without changing the base ModelContextTool contract. Keep the schema mapper private, expose one named derived tool type for downstream declaration emit, and retain schema-less registration.

Typecheck the declaration surface with Vitest against ESNext and the current stable TypeScript compiler while preserving TypeScript 5.0 consumer compatibility.