How to publish to npm using scripts in package.json? - npm

Question

In my project, I have a requirement where I need to publish a package to 2 registries.
Currently, whenever I need to publish, I do the following steps.
npm config set registry https://registry.npmjs.org/ and then npm publish.
npm config set registry http://npm-registry.myorg.com and then npm publish
This becomes a tiring process for me as there are a lot of new changes that I publish. So I thought of reducing some work by creating a script in package.json which can do this automatically.
This is what I added.
{
scripts: {
"deploy:private": "npm config set registry http://npm-registry.myorg.com && npm publish",
"deploy:public": "npm config set registry https://registry.npmjs.org/ && npm publish"
}
}
So when I run yarn deploy:private, it gives below to me
npm ERR! code ENEEDAUTH
npm ERR! need auth auth required for publishing
npm ERR! need auth You need to authorize this machine using `npm adduser`
How can I resolve this, please help?
----------UPDATE-----------
After googling I have found this https://docs.npmjs.com/using-private-packages-in-a-ci-cd-workflow
Based on this I have set my token as env variable and in the project I have created a local .npmrc, with below contents
.npmrc file
//registry.npmjs.org/:_authToken=${NPM_TOKEN}
//npm-registry.tokopedia.com/:_authToken=${NPM_TOKEN_PRIVATE}
But still, I get the error when I try to run the above commands.