Photo gallery with taxonomy filter
This is quite a bit more complicated than your previous question.

My best advice would be that in order to get each content node to have a gallery with multiple images, each Article node should use an image field with multiple values.

These "child sideshows" will be completely separate from the "parent slideshow" which is the one using Views with the taxonomy filters (e.g., "Previous / Next Forest").

You should still be able to make the "child slideshow" into a scrollable gallery as you show in your thumbnails (e.g., "Previous / Next image in Article") by using a library like SlickSlider.

This Drupal.org issue queue talks about setting up Slick without Views as a "multi-imagefield single-node slick on D8" so it can definitely be done. (The Slick Extras module may help, but I haven't tried it so I'm not sure.)

It will be a bit more work this way, and not all the advice you find online will be completely applicable to your situation. If you get stuck, I recommend following the Javascript code in the Slick demos rather than any Drupal-specific walkthroughs.

Good luck!

EDIT 2019-11-27: Thanks, the comment below helps me to understand what you're trying to do.

The real problem is that your data model is a mess: you want to apply the taxonomy terms to the Article (child slideshows) content type, and also to the individual photos within the Articles. You apparently don't want to display all the photos in each Article, but only the individual photos that match the selected taxonomy term in the parent. That wasn't very clear from your earlier description.

To accomplish that, I think you'll need to implement the term filters (Animals, Forest, People) as an exposed filter on the child slideshow. You can't filter by the taxonomy terms on the child node because you want to jumble terms together at both levels.

This is made more complex by the fact that you want the same buttons to act as exposed filters on two different Views. No wonder you are having trouble.

Maybe you can use a contextual filter on the child slideshow that refers to the value of the exposed filter on the parent.