If you want to display a tag cloud with your groups as tabs, you can use the Gutenberg block or the following shortcode:
[tag_groups_cloud]
The output will look like this:
Settings and Parameters
For all available options, see
Filtering of post archives by tag groups
If you use the same tag with various groups and want to make sure, that the tag links only to those posts that use this tag with a particular group, you need to activate an additional filter
Use the toggle switch in the Gutenberg block or in the shortcode the parameter:
add_premium_filter=1