Borrowed Sims 3, still accessible w/o key, but unsure of how to purchase packs

So I have some questions I'd love help figuring out.

I borrowed the Sims 3 from my local library quite a few years ago (so back when the disc was enough and you didn't need a code to "own" the game). I recently wanted to start playing it again, and have a thesims3.com account. However, on there, it doesn't show the base game as something I own, just the one expansion pack I have (Island Paradise).
I thought of trying to purchase and potentially transfer expansion packs from Steam over to the EA app, but Steam will not let me buy the expansion packs since I don't have the base game from Steam specifically (my EA account with the sims 3 and steam are linked).
I'm unsure of what my next move should be. I've heard there's been problems with buying packs from the EA app itself, so I'm hesitant to do so through there, but also that it's potentially no longer possible to transfer the Sims 3 base game from Steam to EA if I were to make a new account to do so. Or if there's just some form of simple solution that would allow me to both get my sims 3 game "registered" through thesims3.com and buy packs from Steam and transfer to EA without needing the base game through Steam.
Any information would be extremely helpful, thank you.