[Fixes #74035678] Split and implement remaining serve stale tests

Because we've realised that the behaviour is different depending on whether
we wait for the health check to mark the backend as down. This was described
in Matt's original varnishtest code:

https://github.gds/gds/fastly-config/blob/177d002bcc33639bbccf61fa52f7809ed4b2d01d/test/feature-tests/serve-from-stale-govuk.vtc#L10-15

Pair w/Cal.