Problem/Motivation
#2352949: Deprecate using Classy as the default theme for the 'testing' profile set a new direction for how to avoid having our tests be dependent on themes that may disappear. It also introduced a BC layer. For now, Drupal core uses that BC layer, and because of that deprecation errors are triggered.
They're suppressed thanks to \Drupal\Tests\Listeners\DeprecationListenerTrait::getSkippedDeprecations().
Proposed resolution
This issue is about removing the suppression of that deprecation error from \Drupal\Tests\Listeners\DeprecationListenerTrait::getSkippedDeprecations() and instead updating all relevant tests.
(This then also unblocks the next step: #3083275: [PP-2] Follow-up for #2352949 and #3082655: update tests whose assertions are implicitly relying on Classy markup to not rely on it anymore.)