bench: varying-slopes reference benchmark vs R fixest (#65)

[schroedk]

What

A standalone, on-demand benchmark that times varying-slopes estimation on shared synthetic DGPs and prints R fixest's fit time + iteration counts. Captures reference numbers before within's slope solver exists (#58/#59), so the implementation slices can be measured against an external baseline.

Not a test: no correctness gating, run by hand.

Design (slim by intent)

• One module benchmarks/slopes_fixest.py + one R worker benchmarks/fixest_fit.R.
• No CLI. main() runs the fixed CASES catalog at a module-level SIZES constant; sweeping scale is a one-line edit.
• No backend Protocol / classes. One run_fixest(case) (the only live arm) + a run_within(case) stub — the documented Varying slopes: benchmark script vs R fixest (within pluggable) #65 seam to fill once the slope solver lands.
• One Case dataclass carries the columns plus fe_terms (which factor holds which slopes) — the one structured thing both the R formula and the future within wiring derive from. Builders self-name from their params.
• Reuses the live benchmarks._problems panel helpers; the DGP slope-injection math is adapted from the (defunct) prototype, and the R worker is recovered from the lost local harness.
• Python owns formula construction (Case.formula() → worker[z1, z2] + year + firm); the R worker just fits the formula it's handed and prints RESULT_* markers (warmup + median-of-n via proc.time(), plus an untimed fixef() slope-recovery sanity count).

DGP catalog

Covers both the topology axis (where within's value lives) and the slope-count axis:

• fixest_{simple,difficult}_v{1,3} — worker×year×firm panel, 1 vs 3 worker slopes, on i.i.d. (simple, R's home turf) vs band-structured (difficult, within's sweet spot) firm membership.
• akm_experience / akm_both — AKM mobility panel (Zipf firms, low mobility, clusters, largest component) with structured experience/tenure slopes.

pixi wiring

R is kept out of the default dev/test/CI env via a dedicated fixest feature+environment (r-base, r-fixest, r-data.table). Run:

pixi run -e fixest bench-slopes     # first run provisions R + fixest

The default env is unchanged.

Reference numbers (n=100k)

case	time_s	iters
fixest_simple_v1	0.027	5/5
fixest_simple_v3	0.038	6/6
fixest_difficult_v1	0.444	186/153
fixest_difficult_v3	1.111	292/255
akm_experience	1.047	295/295
akm_both	3.626	895/975

The simple→difficult jump on an identical panel (5 → 186 iters at V1) isolates topology as fixest's cost driver — exactly the regime within's preconditioned solve targets.

Verification

• R-skipped path: prints a clear "R fixest: skipped" message, no crash.
• Full path: feols fits across the catalog (numbers above); RESULT_FIXEF confirms both slope components recovered on the dual-slope case.
• ruff check + ruff format clean.

Out of scope (per #65)

within's slope solver (#58/#59) — only the stub seam here; Julia arm; frozen fixtures / correctness assertions.

Closes #65.