[meta] Remove Classy testing profile dependency

Problem/Motivation

In #2350823: Use the Classy theme in the Testing profile we temporarily changed the testing profile to use classy theme - instead of stark as we cleaned the css classes out of core and into classes.

Proposed resolution

Return the testing profile to stark and update all the tests as necessary to compensate for the new, stripped down markup.

Remaining tasks

1. Return testing profile to use stark
2. Update all the tests which currently rely on CSS classes such that they are compatible with the classless version of Stark

API changes