Question: Is it legal for my manager to disclose if I am on or off the clock to the general public?
Answer: We always remind people that we are not attorneys or HR specialists. In your situation, the law would have to be a state law, since it does not come under a federal mandate of which I am aware, speaking as a layperson. You should consult the website of your Department of Labor.
However, as a matter of practicality, yes under many circumstances it would be an employer’s right to tell someone if you are “off the clock”, meaning not working. For example, a customer calls and asks, “Is Mark in today?” “When will Mark be back to work?” “What day would be the best to talk to Mark about my (Whatever). In those cases, an employer is providing information that is necessary to do business.