After you create the env, you can add a branch policy by following the steps from their doc at https://docs.github.com/en/rest/deployments/branch-policies?apiVersion=2022-11-28
something like so:
gh api \
-H "Accept: application/vnd.github+json" \
-H "X-GitHub-Api-Version: 2022-11-28" \
/repos/OWNER/REPO/environments/ENVIRONMENT_NAME/deployment-branch-policies