The best advice I can provide here is to, if possible, switch to using behaviours and Mox, following the advice outlined in Mocks and explicit contracts - Dashbit Blog, because this allows to keep async tests, and uses per-process expectations (even if it can be a bit harder to use in some contexts, in my experience), with clear boundaries.
On your specific question, also, without more code it will probably be a bit difficult to provide some help. If you have a way to share a smaller reproduction (and I know it can be hard to do), you will get more chance here! (or a bit more concrete elements).
The overall vibe of these symptoms is “there is something leaking from the execution of one test and affecting the other test”, since they go away when run in isolation.
“If I put a sleep in the failing test that also makes it pass” sounds like a race: something that cleans up the first test is running in parallel with the second test, and if the second test beats the cleanup you get a failure.
I don’t see anything obviously asynchronous in the mock source - this issue mentions switching to ExUnit.at_exit instead of after, but the suggestion was not implemented.