ts problem

class ObjectId { }

namespace Test {
    type Omit<T, K> = Pick<T, Exclude<keyof T, K>>;

    type EnhancedOmit<T, K> =
        string | number extends keyof T ? T : // T has indexed type e.g. { _id: string; [k: string]: any; } or it is "any"
        Omit<T, K>;

    type ExtractIdType<TSchema> =
        TSchema extends { _id: infer U } // user has defined a type for _id
        ? {} extends U ? Exclude<U, {}> :
        unknown extends U ? ObjectId : U
        : ObjectId; // user has not defined _id on schema

    // this makes _id optional
    type OptionalId<TSchema extends { _id?: any }> =
        ObjectId extends TSchema['_id']
        // a Schema with ObjectId _id type or "any" or "indexed type" provided
        ? EnhancedOmit<TSchema, '_id'> & { _id?: ExtractIdType<TSchema> }
        // a Schema provided but _id type is not ObjectId
        : WithId<TSchema>;

    // this adds _id as a required property
    type WithId<TSchema> = EnhancedOmit<TSchema, '_id'> & { _id: ExtractIdType<TSchema> };


    interface Base {
        _id?: ObjectId;
        potato: boolean;
    }

    function insertOne<T extends Base>() {
        const rec: Omit<Base, '_id'> = <any>{};
        ins<T>(rec);    // Problem
        ins<Base>(rec); // Good
    }

    function ins<T>(p: OptionalId<T>) { }
}