You may get a reply from an EA moderator here, but likely not. And, unhelpfully, the help links just re-direct here to the forums. As far as I know there is no way to register Sims 2 games anymore. Those versions simply aren't available online. You'd need a disk drive, and to hope for the best, because they don't always work with no access to the Sims 2 servers.
I originally bought Sims 2 on disks, then eventually registered those disks and started playing without them. The last couple packs I bought were purchased on the EA downloader (that's what it was then). When they switched to Origin, some of my packs disappeared. I contacted customer service, because this was when you could actually talk to a person. I was told those packs no longer existed on their own online, they'd consolidated them into bundles. They gave me a bundle for free to replace some of my missing packs. One, they couldn't give me for some reason. They gave me a Sims 3 stuff pack for free to make up for it. If I hadn't also had Sims 3, I guess I wouldn't have gotten anything. When they released Ultimate Collection, they gave it to me automatically because I had Sims 2 on Origin. Briefly, both versions of the game were there, then eventually only Ultimate Collection.
I paid for Legacy, because I love Sims 2 and felt like it was a reasonable price for an updated game with support. But there is definitely a part of me that acknowledges how unfair it all actually is.