They are perfectly permissible to be carried on trains. The conditions of travel were written at a time before e-scooters were prevalen
I think relying on a non contractual or non legally binding (criminally) website is a dangerous move personally.
I have nothing against the legal use of e-scooters, but the laws and regulations involved go beyond simple contract law or Byelaws.
In any event, a condition of travel or Byelaw cannot override or alter primary legislation like the Road Traffic Act.
I think some also forget that Railways, for the main, are private enterprises, and would be free to refuse carriage to anyone and any item, as they deem fit, so long as a refund is given (if a fare has been paid), and subject to the Equality Act of course.
The second an e-scooter wheel touches the platform surface, you have a myriad of legal requirements (insurance, license etc), as well as the fact a platform isn't a road, so would probably be an offence anyway in most cases. It doesn't matter whether it's folded up or not.
The laws are actually very clear in my opinion, but they are not fit for purpose and need modernising, but there is substantial opposition to these legal scooter schemes as it is.
I personally would support a ban on these being conveyed, because they are not legal to use on roads outside of the trial areas anyway, (except on private land, with specific consent obtained), and I doubt the hire agreements of the legal ones allow them to be taken out of the area anyway. It surely also defeats the point of these anyway that they are for the final mile etc of the journey, you get off the train and jump on one from the docking station at the other end.