Ensure that caching is implemented correctly

From @wim-leers' comment at https://www.drupal.org/project/quicklink/issues/3047931#comment-13089045

While looking at the code, I did spot two problems, both relating to cacheability:

1. $variables['#cache']['contexts'][] = 'session.exists'; should be inside the "if no_load_when_session" branch, to vary correctly — BigPipe does this too (see https://git.drupalcode.org/project/drupal/blob/c779a82a28c2e9f140f6a11db...) — this is still directly related to the originally reported problem
2. $variables['#cache']['tags'] = $config->getCacheTags(); should be added immediately after loading $config to ensure that configuration changes are reflected immediately, without manual clearing of caches :) — this one I just noticed by looking at everything above.