With processes I tend to test in stages:
If the internal computation is complex then have it be handled by another module with pure functions – test those.
Then testing the statefulness of a single process. Start one process per test and assert the interface of the otherwise black box – meaning test whatever the message interface of the process is without ever looking into the process’s state. This might need some accompanying code in the implementation to adjust things like timeouts, third processes being sent messages or access to test specific resources like ecto sandbox.
And the third layer is more integration test style for starting a whole assembly of processes and asserting on their combined public interface (likely still messages). Here individual messages between processes under test are no longer relevant. Only thing counting is that the whole system does what can be asserted on from the outside.
