test(bench): recover the duckdb arm and the marginal-cost pass

[FBumann]

Both were written against #231's branch and kept being committed there after that PR was squash-merged, so none of it reached polars-engine. --duckdb-root, --builds, the loop mode, FOREIGN_ARMS and the marginal-cost table were all absent. My mistake, and it is why #189's headline numbers cannot be refreshed yet.

The duckdb arm runs the engine this branch replaces from its own checkout, its own interpreter and its own bench/_run_case.py — nothing is reimplemented here — interleaved with the other two against one shared parquet cache, with the parity gate spanning all three.

The loop pass answers the question the timings cannot. The harness spawns one process per measurement, so every timing is a first build, and each lane does lazy first-call work: ~180 ms eager, ~21 ms duckdb, ~4 ms here. first is what a caller pays who builds one model and solves it; steady is what a rolling horizon pays for every model after. Both are real.

It measures build and hand-off rather than build alone — linopy defers ~82% of its work to whatever consumes the model, so a build-only loop compares our finished matrix against its placeholder. I published a wrong claim from exactly that flaw and it is fixed here.

Smoke-tested on the current base:

dispatch xs  farkas  first  10.4 ms  steady   5.8 ms  warm-up   4.5 ms
             linopy  first 196.0 ms  steady  14.3 ms  warm-up 181.7 ms
             duckdb  first  43.9 ms  steady  23.4 ms  warm-up  20.5 ms

bench/README.md keeps #233's structure — narrow runs go to /tmp so they cannot clobber the published file — with the three-engine invocation added to the publishing block.

No numbers are published here. The base has moved twice under them (#233, #234) and again with #238, and the linopy pin is now the v1-semantics build rather than 0.9.0. The ladder is re-run separately, against that linopy, and docs/benchmarks.md and #189 are updated from it.

417 passed / 1 xfailed, ruff and pyrefly clean.

🤖 Generated with Claude Code

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