As far as I know if you started playing Spiral Knights with Steam or decided to link your old account with your Steam account you can't ever again login to the browser version. I thought this could be a requirement that Valve put on Three Rings/Sega but now there are other F2P MMOs that have Steam versions but let you freely login to the Steam and non-Steam versions with the same account. AirMech and Realm of the Mad God both let you do this so my suggestion would be to implement the same feature in Spiral Knights.
Login to browser version with your Steam Id
By accident, we already have that.
-Downlaod regualr version.
-Login on forums using steam account.
-Click "connect with facebook"
The game will check forum status (wich is already logged in with the steam accoutn) and work normally.
@Luguiru: I know I can login with Steam to this forum because I'm doing it right now but what I'm asking is to be able to use my Steam account to play the game on the browser. I'm asking this because sometimes I'm on Linux so I wouldn't be able to access the Steam client.
@Little-Juances: I actually knew about this work around and it works even on Linux with Chromium but unfortunately the game "thinks" you are playing from the Steam client and certain features will crash the game (like trying to buy CE). Other games like AirMech let you link your Steam account with a regular in-game account and have progress be shared between the 2 of them, effectively acting as if they are one and the same. If Valve let them have that feature I don't see why Spiral Knights can't be the same.
From personal experience it is entirely possible to log in with a Steam linked account. When you go to log in it has a "sign in with Steam" option. You will then be redirected to Steam and it will ask you to log in with your Steam account. When it accepts your information it will ask you to enter a code sent to the email linked to your Steam account. Copy-paste the code and proceed. You are now logged in with your Steam account and it redirects you back to this forum.
If you want to log into the game through the website with a Steam account after logging into the website with the Steam account it will ask if you want to open it through Steam, because that is how your account has been connected. Open it through Steam if you want to play on that account.
Have some honeydew.