That looks like it has been scratched off to me.

Looks like a pretty old tree, could probably use pruning on general principles.

I'd prune it in February down to the branch collar, leave a small bit of wood to renew it.

Mine sometimes look like this due to freeze,...bark can be dead 2/3 around but there is still enough sap flowing out to a branch.
You can let it be or cut when you see dead all the way.

What about the larger diameter branch that was already hacked off (stub should not have been left)? Unless it was a dead branch that is the reason for the cambium scorch below the cut.

You don't need to take out the branch if it is an important part of the shape of the tree. If it is still vital and generating vigorous growth it can seal of the rotting area and maintain enough healthy cambium to function indefinitely.

I have trees I manage with major scaffolds that have over 50 year old wounds that started like that. It frequently happens when too much wood is removed at one time- particularly during dormant pruning.

If a much larger branch is removed than the one you cut back to there is always some danger of cambium scorch. It is often worth the risk to bring big vigorous apple trees to a more manageable form when renovating them. I've never lost a tree as result of such wounds.

Thanks for all the responses guys,
The top branch was already cut off by the time I bought the house, so I'm not really sure whether the upper branch was actually dead or not.
It's not an essential part of the tree, but it is a nice lower fruit-bearing branch I'd like to keep if possible. I think I'll let it be until it's for sure dead all the way through, or there is a significant reduction in fruit yields on the branch. Again, thanks!

Thanks for all the responses guys,
The top branch was already cut off by the time I bought the house, so I'm not really sure whether the upper branch was actually dead or not.
It's not an essential part of the tree, but it is a nice lower fruit-bearing branch I'd like to keep if possible. I think I'll let it be until it's for sure dead all the way through, or there is a significant reduction in fruit yields on the branch. Again, thanks!