This change is bigger than it needs to be, you only needed to change the visibility.

Created it as a toplevel class. That makes it clear that the handler is a standalone class. Instantiating HttpServer.HTTPMetricHandler might indicate that a server is still involved.
Given that there are good tests, moving a class should not be problem.

I'm not sure how good our tests are here, and I'd don't like splitting logic like this across files too much.

Given that my comments remain unaddressed I'm going to close this off. If you're still interesting in a change that only makes this public, let me know.