Earlier quoted context omitted.
Lets back up: why are you trying to figure out what branch a historical commit was on? What problem does that solve for you? I've never found that information terribly important or interesting.
Say I bisect some issue to a particular commit. Knowing which branch it was made on tells me what issue it was trying to solve, which gives me context for the entire branch. It also means I can easily request all commits made in the master branch, to see what features were merged in recently.
How is the branch name going to give you sufficient information on that anyway? You're going to have to look at the commit message and probably the surrounding history anyway if you want context for the entire branch.
> It also means I can easily request all commits made in the master branch, to see what features were merged in recently.
In this use-case, you're probably viewing some form of "git log" anyway, so it's not hard to turn on the option that shows the tree view, which should make it readily obvious.