the command to get the effective push remote for the branch, e.g., master, is:
git config branch.master.pushRemote || git config remote.pushDefault || git config branch.master.remote
Here's why (from the "man git config" output):
branch.name.remote [...] tells git fetch and git push which remote to fetch from/push to [...] [for push] may be overridden with remote.pushDefault (for all branches) [and] for the current branch [..] further overridden by branch.name.pushRemote [...]
For some reason, "man git push" only tells about branch.name.remote (even though it has the least precedence of the three) + erroneously states that if it is not set, push defaults to origin - it does not, it's just that when you clone a repo, branch.name.remote is set to origin, but if you remove this setting, git push will fail, even though you still have the origin remote