Maybe the person with the 'admin' account (the employer) can add instructions like 'focus on professionalism' that aren't visible and/or can't be overridden by the employee?

That's not a thing yet

It absolutely is. Enterprise plans allow an org-wide managed-settings.json to be imposed, which take precedence over user or project settings.

There's also a whole compliance API, allowing automated policy enforcement (see https://www.anthropic.com/news/claude-code-on-team-and-enter...).

And then there's the growing field of 3rd party policy-as-code tooling available which can also do stuff like this.