Report HTTP stats by endpoint

Currently stats about HTTP endpoints are tracked haphazardly. Some endpoints are tracked from some early code but most are not. All endpoints should be counted and it should rely on the handler to do so.

Start by locating the existing HTTP statistics tracking and the handler path used by endpoints. Trace how current endpoints are counted, then identify the handler-level point that can cover all endpoints. Done means every HTTP endpoint is counted consistently and the existing statistics behavior remains verifiable through tests.

Written by the indexing model from the issue text.