Good opsec usually means you don't do this anyway. Don't use your anonymous browser for anything related to your real persona. In fact, don't re-use the OS between anonymous and public personas. Or even better: Don't re-use the hardware (also goes for networking). There will always be bugs across all levels of software and hardware that could eventually be chained to expose you. But if there is nothing there that could be exposed, you're already much better off by default. Even if that is very hard to achieve in practice.

Usually you have TOR browser for TOR and a standard Firefox for the standard browsing so they already are two sessions.