Question about persistence with different pools

I believe the iRule is processed first so the user will go to pool B based on the app cookie matching the iRule but what about the persistence? Does the F5 know to use the right cookie depending upon which pool the traffic gets sent to?

The iRule is indeed processed first, or at least negates (with the help of OneConnect) the existing persistence if a different pool is selected. The interesting thing about the built-in cookie persistence is that it magically includes the pool name in its name, so each pool will get its own persistence cookie and load balancing affinity will happen according to the defined pool. If you create a cookie persistence profile with a different name, you won't get the ability to create different cookies for different pools.