Do you have a direct link to the gif somewhere that I can use to test further with or a link to the site you’re having the issue on?
This is because WP resizes the image, when it does it only captures a single frame of the gif in the 2000×1000.gif it saves thus removing the animation.
Since you’re using a child theme, you can fix this in the code and force it to use the full image instead of the resized one WP saves.
Copy over /template-parts/page/content-front-page-panels.php from the default TwentySeventeen folder. Inside of that file, look for the following code near the top
$thumbnail = wp_get_attachment_image_src( get_post_thumbnail_id( $post->ID ), 'twentyseventeen-featured-image' );
Modify it to the following
$thumbnail = wp_get_attachment_image_src( get_post_thumbnail_id( $post->ID ), 'full' );
Save your changes and it should then start playing the gif in the panel area.
And for the first background one can do the same modification in /template-parts/page/content-front-page.php
