How to serialize patch request with optionals via json_serializable?

Question

@JsonSerializable
class PatchUserDTO {
  final String? name;
  final DateTime? birthday;

  ...OTHER STAFF...
}

But I need to differentiate between birthday == null and birthday is not set.

I guess, nice solution would be

class Optional<T> {
  final T? value;
  Optional(this.value);

  T? toJson() => value;
}

@JsonSerializable
class PatchUserDTO {
  final String? name;
  @JsonKey(includeIfNull: false)
  final Optional<DateTime>? birthday;

  ...OTHER STAFF...
}

But includeIfNull is applied to finalised json. So if Optional<DateTime> is not null, but value is null, it still won't be serialized.