Contact support.
... try looking at the many other threads in this sub-forum about this where you will find links to help you out. An example:
forums.frontier.co.uk
Purchase/redeem the game to continue
Yesterday i purchased the ED commander deluxe to start playing this game first time in my life... Now i have been trying 2-3hours to fix this and get information. I bought the game through steam, i made new frontier account and linked steam to it. Now i can only play the demo and when i try to...
Search button - type "can only play demo" ... then contact support
If you haven't done already try if you activated the key through steam: right click on elite dangerous, click "View CD Key", go to https://tools.elitedangerous.com/en/register, put in your email and password along with the key and click redeem
Except Steam purchases no longer come with a CD Key.
Im speaking from my experience. I also purchased a code the same way and i encountered the same problem because i only activated through steam. Once i did the steps i listed above it registered it to the frontier account letting me play properly.
I have the exact same problem
Strangely, I bought a new copy of Elite Dangerous + Horizons for Steam via Humble Bundle sale last week and I see that there are CD keys listed whereas my Steam-store bought version has no CD keys. Some weird "jobbie" going on with the Steam versions at the moment.