bench(flow): referral API step under each_item approval + durable, 20 runs per arm

[abrichr]

Stacked on #1364 (the API-step stack). Item 6 of the production-profile task: the measurement.

Label: API step under each_item approval + durable, no run gate; harness answers approvals; approval wait excluded. These are not numbers for the governed production profile. The referral bundle doesn't pass the run gate yet, because of its GUI path (see the admission list in the session notes, and the local-edit proposal #1366).

Results (local OpenEMR test copy, synthetic patients, 2026-10-19)

Arm	Runs	Correct by SQL read-back	Saved through	Median engine time	Approvals per item
API steps off	20	19, plus 1 safe stop (nothing saved)	GUI	15.95 s	2 (1 for r6)
API step	20	20	API 18, GUI 2 (r6)	1.12 s	1

• r6 is the possible duplicate of a seeded chart. The API step's duplicate pre-check found the chart, so the API step was not used; the GUI steps ran and created nothing. That is the right outcome.
• The GUI arm's safe stop was the save's identity check refusing at coverage 0.81 before any click. The earlier spike saw the same stop once in 20 runs.
• No run saved a wrong or duplicate chart.
• For reference, the scoreboard's arm 5 (API step, no gate, not durable) measured 3.2–3.9 s per item. Its timing boundaries differ from this harness's engine_s, so the two numbers aren't directly comparable.

Not covered

The engine is the API-step stack (#1358, #1361, #1362, #1364) at 352af585b, without the review fixes #1367–#1372. With #1370 and #1371, this referral's API step is refused:

• OpenEMR sends a background POST /library/ajax/execute_background_services.php inside the span;
• the form runs submitme(...) on submit and capitalizeMe on each name field, and uses a custom pastDate rule.

Also in this PR

• benchmark/openemr_api_tier/approval_durable.py: the harness. Both arms run under ApprovalGate("each_item") and durable=True, interleaved; a harness approver stands in for the person and the approval wait is measured separately. It gains --from-block, --skip-done and a summarize command. The run paused for a shared quiet window after 19 runs and resumed into a second directory; summarize rebuilds the CSV and summary from the per-item results.
• A fix found by the real bundle: the approval view listed the same record rows once per record check (11 times), which pushed the phone view past its 24-row limit. Each record-check selector is now listed once, both in the view and in the digest. Test included.
• Committed data: results/approval_durable/2026-10-19-combined/ (runs.csv, summary.json, and 40 per-item JSON files), plus a README. The 21 MB of screenshots and engine reports are kept outside the repo, in ~/oa/scratch/api-step-measure/. public-artifacts.json was regenerated with check_release_consistency.py --write-public-artifact-inventory.

🤖 Generated with Claude Code

[abrichr]

Included in batch #1383, which runs CI once for several reviewed PRs. This PR is marked merged when #1383 merges. Please don't push here unless asked; a new commit leaves it out of the batch.