Mass Effect Andromeda "You are not allowed access to online features"

Yes, another one of these. After spending many hours over multiple days discussing this issue with both EA and Steam support I was finally told to just report my issue here. In short, you have probably heard this one before.

When I boot up Mass Effect Andromeda it greets me with the error message "You are not allowed to access the online features of this game". After following the steps outlined in this ( [PC] Mass Effect Online Access Error in Multiplayer Mode | EA Forums - 9200656 ) forum post to no avail I contacted the EA support for the first time. Over the course of a few hours with multiple support agents attempting to help the end result was, that their internal system does not recognize me owning the game in the first place. They instructed me to reach out to Steam support since I had bought the game through them and ask for "the specifics of the purchase" (The automatic translation making it quite difficult to actually follow what exactly they were trying to tell me by the way). So I did just that, with the Steam Support getting back to me after two days stating that on their end all is fine, I own the game and it is registered in their system. Great, back to EA support I was sent.
I explained my issue for what felt like the 100th time and eventually the support agent figured out that yes, indeed, their system does not recognize any ownership on my account of a product key regarding Mass Effect Andromeda. After telling me that they would help me if they could, they said they would report it to their internal team and sent me here to report my issue once more, hence this post.

I have seen multiple posts about this reaching back many years. Some are marked as resolved, others aren't. Lets see my luck