experiments: count backend round-trips per user action

Answers 'are we batching or paying a round-trip per item' with numbers.
Wraps CodeModeClient.invoke on a live pilot and reports calls + wall + ops
for each action.

The trap it encodes: ListingView._grow streams the whole segment on a worker
thread, so it lands calls continuously regardless of what the user does. A
naive census attributes that to whichever span is open and every action comes
out at a near-identical '~1 call per 10ms of pause', which measures the pause
and not the action. It now drains the grower first, reports it as its own
line, and measures the rest against a quiet backend.

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