As I stated in the title, I'm able to share my filters and dashboards with other groups in Jira, only when I'm in the group too, which is very weird. For example there is a group "company-management", and only when I add me into this group, I can see this group in the dropdown field. So that means, I see only the groups, where I'm as member in them.

Global permisssion seems however fine, and it's Jira cloud instance (paid version).