If you want to display a tag cloud with your groups as table columns, you can use the Gutenberg block or the following shortcode:
[tag_groups_table]
The output will look like this:((We are here using custom styling for the tags.))

Settings and Parameters
For all available options, see
Demos
You can see examples of these shortcodes in action on the demo pages.
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=0
If the resulting list is unexpectedly empty or misses posts, please try to run Maintenance.