Deanonymization is easy as hell. Even if they can’t link your torrenting to your web sessions immediately, they can get logs from the VPN provider, threatening to hold the VPN responsible if they don’t release this information, and see that you were in fact torrenting. And if you think there’s no log because the VPN provider told you there’s no log, you’d be wrong. They are in fact required to log and keep logs temporarily for “lawful intercept” purposes, and if asked by government to monitor you, they may be required to keep logs of your activity indefinitely. I say “indefinitely” rather than “permanently” because they may be allowed to purge the logs after they hand them off to the government, or after the order is over, etc. And they are required to keep you from knowing you’re being monitored, so the common practice is to claim a no-logs policy “unless required by law”, protected by gag orders.
They will then see:
-What trackers you connected to
-What peers you connected to
-What websites you connected to
What they will not see unless this VPN replaced your root certificate, is the contents of any encrypted connection you make to peers, trackers, or websites. That being said, if you need a proprietary app to connect to the VPN, it’s probably replacing your root certificate so it can see your encrypted traffic, likely as part of that “lawful intercept” requirement.
That being said, they won’t go through such effort, as they already have Facebook, Twitter, and other Big Tech media with cross-site tracking to identify you regardless of your VPN session.
But since torrenting isn’t web, if you put your torrent client behind a VPN while browsing without one, you’re a lot safer, and you’ll just have to hope your VPN provider isn’t watching for torrent activity like your ISP may be.
Now if a copyright holder or copyright troll is willing to spend the extra time, and the VPN provider hasn’t discarded the logs yet, they could still rat you out, as they’ll be asking who connected to X tracker and Y peers at Z time. But if that’s who you’re up against, the only winning move is to go get a cup of coffee or borrow someone’s wifi. That all aside, with a subreddit full of people using VPNs to torrent, chances are it’s a dead end for most copyright holders.