Links should have a discernible name per https://dequeuniversity.com/rules/axe/4.10/link-name
Thus re-use the existing tooltip text with the name of the badge as the aria-label text for the badge's <a> link.

Ref T16072

Set up a badge at http://phorge.localhost/badges/.
Award badge to some user at http://phorge.localhost/people/badges/1/.
Make that user who received a badge comment on a Maniphest task.
Hover over the badge below the user avatar next to the comment to see the badge name.
Inspect the <a> element surrounding the badge icon below the user avatar next to the comment, see an aria-label also set to the badge name.
Optionally, run an Accessibility check in Chromium Lighthouse.