This is not a feature I have ever seen on the GitHub web interface directly.
I only know it through my 2009 answer which was linked in the comments above, but it does not apply to your question.
You have dedicated URLs for comparing commits, but not for listing branches including a given commit.
One alternative/workaround on GitHub website would be to use a GitHub Action triggers by a pull request: the action script would then list the branches which include the commit from which you are doing a PR (to a dedicated dummy branch of your repository), since you can do such a PR directly from GitHub web UI.
But that seems a bit far fetched.