The process I went through was the following:
1) Created an account in swtor.com.
2) Activated the security key on swtor.com's account.
3) Added the Game to Steam library.
4) Bought the 30 days subscription.
5) A notification appeared on the Steam page of the game, telling me that the subscription package would be automatically "installed" when I played the game.
6) Clicked "Play" the game on Steam.
7) I ran into the launcher failure bug. After a while, I fixed it by using the repair function of SWTOR_setup. This initially caused the launcher to start while bypassing Steam. I closed it, and then re-launched it through Steam.
8) The launcher opened up, prompted me to insert my swtor.com's account profile, password and key. I did so.
9) I started the game from the launcher.
10) The game started, but no subscription was activated. I created a test character to see if it would help, but to no avail.
11) Through these various phases of trial, I routinely went to https://account.swtor.com/en/account, and noticed that no Steam account was linked.
12) While on Character Selection screen, I tried clicking on the Customer Help Service Center, but the only action that it allows me to perform is to click a Subscribe button, which just links me back to the game's main Steam page.
I can send another email with the requested screenshots proving the purchase of the subscription, but the Steam account not linking to the Swtor one seem like an issue independent of the subscription (though it prevents me from using it). There are no previous accounts, as I said earlier, I never played this game before. In fact, testing by trying to create a second account now resulted in failure, since the email already has the main one associated with it. I've already tried reinstalling the game, verifying game cache, logging in/out of both swtor account and Steam. The accounts do not link. Is there no process to force a link by providing both Steam and SWtor profiles? It seems like this should be a straightforward process, like linking the EA and Steam accounts...