i can’t imagine adding a button there would be too much work. i think the link to the report for the group will always be the query number (you can see it in the admin query page URL) appended at the end of /g/[group-name]/reports/. so a report at /admin/plugins/discourse-data-explorer/queries/-15?params=null should be at /g/[group-name]/reports/-15. since queries can be shared with multiple groups, the share link would need to accommodate that somehow to generate a distinct link for each group - i think seeing the groups listed as well would help, since it is theoretically possible you may not want to share the link with all groups in the list. 
i may take a stab at a PR for this later today if i am adventurous and my job searching continues to be futile.