[devtools] qunit: use new async testing APIs
http://qunitjs.com/cookbook/#asynchronous-callbacks
QUnit keeps track of all the assert.async() objects created inside the
test functions and expects all done() functions to be called. Failure to
do so will result in the test being failed.
Unlike .start and .stop which were internal APIs, assert.async() is
stricter and fails tests if assert methods are used *after* all done()
functions are called (see "test callback execution order").
Related to #5533333.
