Make sure you have permission to publish, by running
npm access ls-collaborators
While on the master branch, switch to a new branch, possibly called release:
git switch --create release
npm run make-release-commit
Create a new pull request from this branch. The name of the pull request possibly identical to the commit message.
"Rebase and merge" the pull request.
git switch master
git pull
Where $VERSION is the new version, run
git tag v$VERSION
For example:
git tag v5.2.4
And then
git push --tags
npm publish