Perhaps via an environment variable such as $SRHT_GIT_BRANCH.

For example I want to know if this is master branch so that I can update a download page with uploaded binaries. Or if it's a non-master branch I want to create an alias from that branch name to a download link.

Here's how I do this with Azure Dev Pipelines today:

https://github.com/ziglang/zig/blob/9801a1df6a6a55bb98cb4141d7e8f7340f324de2/ci/azure/linux_script#L33