Add content from HttpKernelUiHelperTrait::drupalGet() to $this->content, use AssertContentTrait

Joachim Noreikorequested to merge
issue/drupal-3582985:3582985-set-content-from-drupalGet into main

Closes #3582985

Cherry-pick some of the changes from https://www.drupal.org/project/drupal/issues/3582580

Edited by Derek Wright

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