I honestly wouldn’t worry that much about it, the different tabs are working in their own environments that makes it more difficult for info from one to be taken by another, if you use any basic opsec, i.e. closing unnecessary tabs, different user names/passwords, a vpn, even a freepn you should be okay. If you’re still worried about it you could use a temporary card (something like privacy.com), you could also use tor for your piracy, if it’s not the most secure browser its up there. Just be ready for slower download speeds.

If you’re using firefox on desktop your tabs are sandboxed and should be isolated from each other. It is possible to break that sandboxing though.

Locks have only ever been good for keeping honest people out. If someone really wants into your home, safe, toolbox, etc. there’s always another way in.