[code-infra] Proposal: Move publishing action to mui-public

[Janpot]

Trying to come up with a strategy that is less breaky, and requires fewer backports as the publishing logic evolves. Is there really a need to have this logic in every repository?

• Centralize a single action for all packages. Always publish from mui-public master. Check out the repo in question and use the release:build command to create the production bundles. Use the mui-public logic to publish them.
• The single contract between the repo to be published and the publishing flow becomes "check out repository at commit X, then run release:build"

Questions:

• Current actions restrict execution to specific team members through GH env, how would we handle this?