So, I downloaded SWL from Steam. I told it my Funcom account name, and from there transferred all the goodies I'd bought for The Secret World to SWL. They didn't show up. I waited a few days as it might have been something that took time to process, but nothing happened. I put in a petition to speak to a customer service representative (which is why I'm using the SWL acronym — that's what the CSRs use) and it was all explained to me.
The version of SWL you get from Steam sets up a new account. It's not the same as the Funcom account. You need to download the client from Funcom to use the Funcom account. It's possible to link the accounts together, so that the Funcom account overwrites the Steam account, but it does overwrite it: your character is lost (no biggie) and your patron status is lost (hey, I paid 1p short of £10 for that!).
I'm therefore downloading the Funcom client (using my slow BT Internet connection, so I don't go over the limit for my faster connection again). I'll wind up with two versions of SWL on my PC: the Steam one and the Funcom one — plus the copy of The Secret World that's still around from 2015. I'll mail all the useful goodies from the patron account to the non-patron account for a month, then let it lie fallow.
All this would have been so much easier if I'd read the instructions.
Of course, reading the instructions would have been so much easier if I could have found them before I started.
