I thought BA's website and app were bad, but I have a new-found respect for them after using KLM's in earnest for the first time in a couple of years.

Not only does my EB number not get properly saved, but try the same thing with your contact email address. That also pretends to be saved, but when you go back into passenger details is wiped.

SAS, as above, shows my EBG number correctly, but the AF website refuses to show any Slyteam benefits (check-in luggage on LIGHT fare, seat selection). Online check-in is no better, so I cancelled it. I'll do it all at the airport tomorrow. Lounge access should be no problem, as the lounge staff appear more clued-up than KLM's support team, but I have a bag to check in.

I'm assuming showing EB gold to someone on the check-in desk will be sufficient. I'll update here

EDIT: I reached out to KLM's WhatsApp support and they fixed it. They confirmed that my EB number was added and also that no status benefits were showing. So they re-added the EB number. I'm now checking in and not only is the EB number showing under my name but all the benefits - lounge, luggage on light fare, seat selection - are now correct.