Replace the washer in one of the toilet angle stops. If no change,replace ballcock or install new ballcock kit. The noise is caused by a loose or worn washer at a point where pressure changes.

Any time I have a water system noise issue I will let the noise start and then sequentially turn off each fixtures supply valve until the noise stops. That tells me which fixture is the problem.

Will the clatter harm the plumbing or is it harmless noise?

I never heard of it breaking a pipe but the valve,facuet,ballcock or wherever the loose washer is will soon become inoperable and will not turn water off.