Follow-up to #44443.
This helps investigating the cold-start timeline, and could be used
by tooling to A/B compare branches affecting the cold-start time.
Additionally also change the `handle_request::select` span, so that we
can see the blocked time (which was probably what was intended), since
the actual time spent on recv after select is insignificant.
Testing: Tracing output is not covered by automatic tests.
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Signed-off-by: Jonathan Schwender <schwenderjonathan@gmail.com>