Can not satisfy the type for generic middy middleware

Question

I want to have a custom middy middleware which parses the event.body with zod and saves it already typed to the request so that it can be used in the handler.

This is what I have so far:

export interface TypedAPIGatewayProxyEvent<T extends ZodType> extends APIGatewayProxyEvent {
  middy: {
    event: {
      typedBody: z.infer<T>;
    };
  };
}


export const parseBody = <T extends ZodType>(
  schema: T
): middy.MiddlewareObj<TypedAPIGatewayProxyEvent<z.infer<T>>, APIGatewayProxyResult> => {
  const before: middy.MiddlewareFn<TypedAPIGatewayProxyEvent<z.infer< T>>, APIGatewayProxyResult> = async (request): Promise<void> => {

    const typedBody = schema.parse(request.event.body);
    request.event.middy = Object.assign({}, request.event.middy, {
      event: Object.assign({}, request.event.middy?.event, {
        typedBody: typedBody
      })
    });
  };

  return {
    before
  };
};

However whenever I want to use it in the handler like this:

const schema = object({
  email: string(),
  password: string(),
});

export type schemaType = TypeOf<typeof schema>;



export const handler = async (input: TypedAPIGatewayProxyEvent<typeof schema>): Promise<APIGatewayProxyResult> => {
  const lala:schemaType = input.middy.event.typedBody;
  
  return {
    statusCode: 200,
    body: JSON.stringify({
      email: lala.email,
      password: lala.password
    })
  };
};

export const lala = middy(handler)
  .use(jsonBodyParser())
  .use(parseBody<schemaType>(schema)); // Typescript Error

I get the following error:

TS2344: Type '{ email: string; password: string; }' does not satisfy the constraint 'ZodType<any, ZodTypeDef, any>'.   Type '{ email: string; password: string; }' is missing the following properties from type 'ZodType<any, ZodTypeDef, any>': _type, _output, _input, _def, and 29 more.