test: stabilize flaky Poisson(10) niterations convergence test

[bvdmitri]

Problem

The Poisson projection convergence test fails intermittently in the ExponentialFamily.jl downstream CI job (e.g. run 28360311006). The failure is in the Poisson(10) case of test/projection/projected_to_poisson_tests.jl.

Root cause

test_projection_convergence runs a niterations convergence sub-test that sweeps niterations = 100:50:1000 with a fixed niterations_nsamples = 700 Monte-Carlo samples per run, then test_convergence_to_stable_point requires the tail's rolling std to fall below stdthreshold = 5e-2.

For λ = 10 the Poisson variance is large, so 700 samples leave a KL noise floor right at the 0.05 threshold. The test is deterministic (everything is StableRNG(42)-seeded) so it does not randomly flip — but it sits on the pass/fail boundary, and small numerical drift from a different ExponentialFamily.jl / Julia / BLAS version in the downstream job tips it over. That is what makes it look flaky.

The companion nsamples sweep already runs up to 4000 samples and passes, confirming more samples is the correct lever.

Fix

Raise niterations_nsamples from 700 → 4000 for the Poisson(10) testset only (matching the nsamples_range ceiling that already passes). No shared helpers, other distributions, or convergence criteria are touched.

Verification

Reproduced the exact CI failure locally (same max div = 0.278) and swept sample counts:

niterations_nsamples	result	tail rolling-std (w5 / w10)
700 (old)	❌ fail	0.073 / 0.091
2000	✅	0.034 / 0.028
4000 (new)	✅	0.015 / 0.014

All three Poisson test items pass locally (8/8). The Poisson(10) item is slower (~12s vs ~4s), an acceptable cost for the ~3×-below-threshold margin.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.42%. Comparing base (3ed0092) to head (6ab2fd4).

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #98   +/-   ##
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  Coverage   99.42%   99.42%           
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  Files          14       14           
  Lines         520      520           
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  Hits          517      517           
  Misses          3        3           

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