If I'm loking at a commit on GitHub (for example), how can I tell what branch that commit is associated with?
Your wish is their new feature
If the commit is not on the default branch, the indicator will show the branches which contain the commit. If the commit is part of an unmerged pull request, a link will be shown.
Once the commit makes it to the default branch, any tags that contain the commit will be shown, and the default branch will be the only branch listed.