Backport of elastic#45794 to 7.x. Convert most `awaitBusy` calls to
`assertBusy`, and use asserts where possible. Follows on from elastic#28548 by
@liketic.

There were a small number of places where it didn't make sense to me to
call `assertBusy`, so I kept the existing calls but renamed the method to
`waitUntil`. This was partly to better reflect its usage, and partly so
that anyone trying to add a new call to awaitBusy wouldn't be able to find
it.

I also didn't change the usage in `TransportStopRollupAction` as the
comments state that the local awaitBusy method is a temporary
copy-and-paste.

Other changes:

  * Rework `waitForDocs` to scale its timeout. Instead of calling
    `assertBusy` in a loop, work out a reasonable overall timeout and await
    just once.
  * Some tests failed after switching to `assertBusy` and had to be fixed.
  * Correct the expect templates in AbstractUpgradeTestCase.  The ES
    Security team confirmed that they don't use templates any more, so
    remove this from the expected templates. Also rewrite how the setup
    code checks for templates, in order to give more information.
  * Remove an expected ML template from XPackRestTestConstants The ML team
    advised that the ML tests shouldn't be waiting for any
    `.ml-notifications*` templates, since such checks should happen in the
    production code instead.
  * Also rework the template checking code in `XPackRestTestHelper` to give
    more helpful failure messages.