This is a similar question to github "Automatically delete head branches" for multiple repositories. In that case, the gh command can be used in a loop to configure the option across multiple repos. The gh cli has these options for the repo edit subcommand:
--enable-merge-commit Enable merging pull requests via merge commit
--enable-rebase-merge Enable merging pull requests via rebase
--enable-squash-merge Enable merging pull requests via squashed commit
Is it possible to disallow merge-commit and rebase-merge programmatically? Or to put it another way, is it possible to only allow squash-merge?
REST API (or other API) would also be acceptable.
When in doubt, RTFM: https://cli.github.com/manual/gh_repo_edit
gh repo edit <username>/<reponame> \
--enable-merge-commit=false \
--enable-rebase-merge=false \
--enable-squash-merge=true
The =true on the last line is optional but included to be more specific.