figure out how they gained access to the account. if they do earn a game or vac ban, the ban will be permanent. it does not matter who was using the account when it earned the ban

If you've reported that to EA they will likely disable your account until they have proof you're the account holder - so you probably don't have to worry about VAC bans.

EA games don't use VAC.

It might be worth finding out how they did that, considering that they need access to your emails in order to do it. SO it is very likely they hacked your emails too.
I got an email from ea as well with a verification code some days ago, so someone probably tried the "password forgotten" feature on my account as well. Obviously didnt work... It was very suspicoius as I hadnt used Origin/EA in more than 5 years.
Maybe check if your email or password were exposed: haveibeenpwned.com

Dear OP, you should be able to communicate with EA with your last e-mail / show them proof of purchase / receipt(s) or something and get your account back - especially since it's linked to Steam.

Hope you get it sorted soon!

PS: I think the only way you could get a VAC ban is by launching an EA product from a linked Steam account.

Originally posted by 𝓁 λ 𝓂 𝒷 𝒹 𝒶🌴:

PS: I think the only way you could get a VAC ban is by launching an EA product from a linked Steam account.

Not at all, no. That's not how VAC works and EA games don't even use VAC.

Originally posted by cSg|mc-Hotsauce:

Originally posted by 𝓁 λ 𝓂 𝒷 𝒹 𝒶🌴:

PS: I think the only way you could get a VAC ban is by launching an EA product from a linked Steam account.

Not at all, no. That's not how VAC works and EA games don't even use VAC.

:nkCool:

Well, that's right eh.. EA doesn't have Valve Anti-Cheat.

So I guess the OP still has control over their Steam account - therefore; no worries on a VAC front!