Just a couple of points (no fix here, so save yourself some reading if that's all you want):

Firstly, I could not log into steamcommunity.com via my browser to update my scrap.tf profile from Steam (I thought this might let scrap.tf know I was indeed a member, as it's been a while since I refreshed my scrap.tf profile this way) - this 'bad login' behaviour is unusual. It was, and still is, reporting incorrect username or password at third-party browser logins.

Secondly, to circumvent the browser login problem I surfed to scrap.tf via Steam's own internal browser, using Big Picture mode. I was then able to refresh my scrap.tf account directly from steamcommunity.com without a manual login, but this still did not resolve the group membership issue that the raffle is throwing up.

The first point for sure shows that something is up with Steam. The second point is, in my eyes, a soft pass for the correct functionality of scrap.tf - as it's still able to interact Steam's API when not hampered by point one. To my mind the problem is, right now, in Steam's lap.