The first time Ui Icon block is displayed, JS is not called

The demo bootstrap fixture is unstable because of missing dependencies, the icons are loaded from some specific icons packs. That's why you have the block 'icon' without the icon loaded.
To work properly it needs from https://gitlab.com/ui-icons/ui-icons-example: ui_icons_drupal, ui_icons_fontawesome (with lib, see readme), ui_icons_heroicons (with lib).