Probably the house icon as in go back to home, the default view.

I thought about that but “home” feels like the root, but it could just be a sub folder of a different branch, still not “home”

Well, yeah, but at the same, there are two big problems with the current icon:

It does not represent upstream. This is the icon for merging from the GitHub Flow (it's on my T-shirt 😂).
Even if there was an icon for upstream, it doesn't relate to changing the branch.

An alternative icon would be the commit icon as it's closest to "branch".

I would actually suggest just putting HEAD there instead of an icon.

I would actually suggest just putting HEAD there instead of an icon.

I think HEAD is actually just whatever you're looking at now, you're always on HEAD

An alternative icon would be the commit icon as it's closest to "branch".

Yeah that wouldn't be bad. An alternative perhaps would be a left or up arrow, kinda like "go back to main".

How about a simple back chevron?

When looking at the upstream repository refs/remotes/origin/HEAD would be the main branch, not the upstream branch of your currently checked out branch locally.

👍 for the chevron as well. However, it would move the branch selector from its default position when present if it's on the left side.

it would move the branch selector from its default position when present if it's on the left side.

True, but I think it's not a big deal since the branch selector is very wide and the movement is of about 30px. What do you say? I think it's less nice on the right side pointing back to the current branch.

Temporary caching in 4bc8bdb enables it on files as well :)

When I'm on a forked repository and hover over the button a tooltip suggesting that it would link to the origin's respective branch appears. However, the link doesn't lead there. It leads to the branch on the current repository (often the same page).

Example from my refined-github fork, I expect the button to link to /sindresorhus/refined-github:

<a
  class="btn btn-sm tooltipped tooltipped-ne BtnGroup-item"
  href="/shroudedcode/refined-github"
  aria-label="Visit the default branch (sindresorhus:master)"
> ... </a>

That's confusing and not what's supposed to happen, right?

It’s-a-bug and I got you pal #1132