I learned that RepositoryBranch is the only NuGet Pack-related property not populated already by the .NET SDK+SourceLink. So instead of going for a full-blown (and typically over-blown) solution for build/assembly versioning from Git information (such as GitInfo or GitVersion or the myriad others), you can trivially pass in this value from your CI script with:
This works in all OSes if you're running with a bash shell. On a Windows agent, you'd need to opt-in to that using shell: bash on the run action (if you're using GitHub Actions). Or you can also just default to bash for all run actions.
NOTE: the wildcard instead of heads is so that this also works for tags, in which case the "branch" will be the tag name.