Collect timing information during runs

This is slightly tricky as we don't synchronously wait for responses, which may arrive in later messages read from the stream -- especially so if we move away from reading from implementations line-by-line.

But it'd be nice to time how long it takes to get responses back.

No file, test, or entry point is named in the issue. Start by tracing how runs send requests and later consume responses from the stream, then determine the timing boundaries and how asynchronous responses should be attributed. Done means timing information is collected reliably without synchronous waiting.

Written by the indexing model from the issue text.