Add option for distributed traces in test proxy

After discussion with @heaths , I am adding an item to enable distributed tracing in test-proxy. We should take the opportunity to utilize structured logging for these messages as well.

When flag `--distributed-trace` is passed, the proxy should generate trace messages in stdout that other applications can consume.

This will probably require a refactor of logging _in general_ in the proxy to get all these outputs figured out

Start by locating the test-proxy entry point that handles the `--distributed-trace` flag and the proxy's existing logging paths. Determine how trace messages should be emitted to stdout for other applications and how structured logging should cover the relevant outputs; the work is done when the flag produces consumable trace messages and the logging behavior is defined consistently.

Written by the indexing model from the issue text.