The Django test runner is trying to create a database, but can't. To get it to work, create a database from the databases tab that has the name that is your main Django database name with "test_" prepended.
You can also use sqlite to run your tests instead. This is faster to run tests, but there are sometimes differences between sqlite and mysql that you need to be aware of. At PythonAnywhere, we use sqlite for most tests, but there are tests where we know that they will fail unless they're run against mysql and there are a few times where we've been surprised by a test failure in our integration loop because that always uses mysql.
That's really something we need to put into the docs or an FAQ somewhere.