If you were willing to bring additional zod tooling or move to something like TypeBox (https://github.com/sinclairzx81/typebox), the json schema would be a direct derivation of the tools' input schemas in code.
The json-schema-to-ts npm package has a FromSchema type operator that converts the type of a json schema directly to the type of the values it describes. Zod and TypeBox are good options for users, but for the reference implementation I think a pure type solution would be better.