Hello Valentin,

Thank you for getting in touch with us!

As I see there is a javascript error on your site, which is not related to LayerSlider but it can cause problem with the initialization of it.
With the update to WordPress 5.5, a migration tool known as jquery-migrate will no longer be enabled by default. This may lead to unexpected behaviors in some themes or plugins who run older code. You should try this plugin for a temporary solution until the theme developer fixes it:https://wordpress.org/plugins/enable-jquery-migrate-helper/

After that the slider should work properly. Please check it.