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Image styles are served by Drupal when they are first created, but then saved on disk. So, the are served up by your webserver directly aferwards. That makes this more of a Varnish question, but I am leaving this open as it is a Drupal related quirk/issue with how image styles work and Varnish.
Very odd. How about composer why drupal/core:8.2.x-dev? Since it isn't in your main composer.json, drupal/core:8.2.x-dev is somewhere in the dependency tree. You can also read the lockfile and search for that and see what section / package is listing it.
Can you show what composer why-not drupal/core:8.6.13 lists? This may narrow the problem down better. As a side note, I suspect there is a Symfony related dependency problem. Personally I always use webflo/drupal-core-strict, pinned top the same version as core, which tends to prevent dependency problems.
Can you try editing composer.json and adding "webflo/drupal-core-strict": "8.6.13" as a requirement, and then doing composer update? If this works, I'll writeup a better answer about what may be going on.