Per https://docs.tangled.org/spindles#environment there should be a TANGLED_REPO_DEFAULT_BRANCH env var available in spindle workflow runs.
When I add this to a workflow:
echo "DEBUG: TANGLED_REPO_DEFAULT_BRANCH='$TANGLED_REPO_DEFAULT_BRANCH'"
It does not appear to be populated:
DEBUG: TANGLED_REPO_DEFAULT_BRANCH=''