How do I hide the “not assigned” button in the Shuffle Box?

The “not assigned” group is the default group for all tags and it has the ID 0 (zero).

In the Gutenberg block

Find the menu where you select groups that should be excluded and add “not assigned”.

In the shortcode

Add to the shortcode exclude=0. If you need to exclude more groups, you join the IDs into a comma-seperated list: exclude=0,1,4.