@xboxbabe70 Necro'ing, or necroposting, is replying to a thread that's been dormant (dead, hence the term) for a long time. It's considered bad form for several reasons, among which is that the details of the conversation may have changed in the intervening years. Another reason is that the original poster has probably moved on and may not appreciate getting notifications for the replies and tags.
It would be incredibly inefficient and time-consuming to manually close all the old threads, and I doubt an autolock function is high on anyone's priority list here. So we have to resort to asking that people not necro and splitting their posts when it does happen.
It sounds like EA_Lanna has looked into your case and confirmed that you were helped appropriately. I don't know the details myself, obviously, but it's not surprising that a code purchased cheaply from what sounds like an unauthorized third-party seller would be cancelled. Many of these sellers will buy from just about anyone, including people that may have originally stolen the codes from EA or otherwise fraudulently obtained them. When EA identifies a code for which it was never paid, it deactivates the pack, regardless of what the player knows about its origin. That's why it's always better to buy from an authorized vendor; EA_Lanna provided you a link.
There is no reason that TS3 would run worse in Steam than in Origin. In fact, Origin's online component takes some resources that you're better off devoting to the game. The difference is small for most people; others put Origin into offline mode and don't worry about it. But playing with all packs could definitely slow down your game, especially if you're playing on underpowered hardware. If you want to know how your computer can be expected to handle the most demanding packs, you can post a dxdiag here.
https://help.ea.com/en-us/help/pc/how-to-gather-dxdiag-information/
Finally, you can still play your owned packs in Steam, if you want. Registering the codes in Origin doesn't cancel your ownership in Steam. The game has to be cleanly uninstalled before it's reinstalled, but you don't have to rebuy anything (aside from the packs that were refunded, of course). So if you wanted, you could try out playing in Steam and buy more packs as you went along. Your saves would also transfer over, although any that you had played while Pets was installed would probably not load unless you bought that pack again.