Difference in type & parse result

[dinfer]

I want to create a zod instance to describe an object, whose keys should not be "$and" and the value should be a string or a number. This is the simplified code I wrote, It works fine in type check, but the success is false.

    const ZRecord = z
      .record(z.string(), z.union([z.string(), z.number()]))
      .and(z.record(z.enum(["$and"]), z.never()));
    type IRecord = z.infer<typeof ZRecord>;
    const zinvalid: IRecord = { $and: 1 }; // Type 'number' is not assignable to type 'undefined'.ts(2322). this is want I want
    const zvalid: IRecord = { a: 1 };
    console.log(ZRecord.safeParse(zinvalid)); // {success:false}
    console.log(ZRecord.safeParse(zvalid)); // {success:false}

    type TRecord = { [key: string]: number | string } & {
      [key in "$and"]?: never;
    };
    const invalid: TRecord = { $and: 1 }; // Type 'number' is not assignable to type 'undefined'.ts(2322). this is want I want
    const valid: TRecord = { a: 1 };

The final goal is to create a zod instance for valid data like this

    type TFilter =
      | ({ [key: string]: string | number } & {
          [key in "$and" | "$or"]?: never;
        })
      | ({ $and: string[] } | { $or: number[] });
    const tvalid1: TFilter = { a: 1 }; // normal keys is string or number
    const tvalid2: TFilter = { $and: ["key"] }; // the value of special key '$and' is a string array and this is the only key allowed here
    const tvalid3: TFilter = { $or: [1] }; // the value of special key '$or' is number array and this is the only key allowed here