fix(integrators): restore the multi-state BilinearIntegrator constructor

[aarontrowbridge]

Fixes #138. Unblocks Piccolo #300.

What

The c9fdeb7 refactor dropped BilinearIntegrator(G, traj, xs::AbstractVector{Symbol}, u); today's only constructor took a single x::Symbol, so stacked-state callers — Piccolo's exported VariationalKetIntegrator/VariationalUnitaryIntegrator, which pass vcat(ψ̃, ψ̃_variations...) — threw MethodError on every call (silent: zero callers ecosystem-wide until the Piccolo coverage campaign found it).

How (additive, following the codebase's existing x_names convention)

• Struct gains x_names::Vector{Symbol}; x_name::Symbol stays as the primary (first) name — existing field access and Base.show keep working.
• New BilinearIntegrator(G, xs, u, traj); the single-name constructor delegates via [x].
• evaluate!/eval_jacobian/eval_hessian_of_lagrangian gather the stacked state across all names (component ranges hoisted out of the ForwardDiff closures — one lookup per call instead of per-FD-eval).
• get_nonlinear_constraints: x_names checked before x_name, so an integrator carrying both fields sums the whole stack. Single-name behavior unchanged (x_names = [x]). Branch coverage preserved via a new x_name-only mock.

Verification

• New testitem: a split-component trajectory (:a, :b occupying the same flat slots as the reference :x) vs. the single-component reference — identical residuals, Jacobians, and Lagrangian Hessians on coinciding flat data, plus test_integrator gates and get_nonlinear_constraints length parity.
• Full local suite green (Pkg.test, 2026-08-21).
• Formatter: 2.12.6-clean (CI's pinned-by-latest arbiter).

Notes for reviewers

• The generic eval_jacobian(::AbstractBilinearIntegrator) now requires x_names; every existing subtype (TimeDependentBilinearIntegrator, Piccolissimo's exponential family) overrides these methods, so no behavioral change reaches them.
• Versioning: 0.10.1 — additive constructor + new field; .x_name still present. Piccolo 2.0.3 follows with the variational integrator tests (Piccolo #300).

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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[github-actions]

⚠️ Performance Alert ⚠️

Possible performance regression was detected for benchmark 'DirectTrajOpt.jl convergence'.
Benchmark result of this commit is worse than the previous benchmark result exceeding threshold 1.20.

Benchmark suite	Current: f29bb9a	Previous: 0cd7923	Ratio
xgate_convergence_ipopt_N51 [infidelity]	7.749323405192854e-11 infidelity	4.429490108037726e-11 infidelity	1.75
xgate_convergence_madnlp_N51 [infidelity]	2.4334978476758806e-12 infidelity	3.086420008457935e-14 infidelity	78.85

This comment was automatically generated by workflow using github-action-benchmark.

[github-actions]

⚠️ Performance Alert ⚠️

Possible performance regression was detected for benchmark 'DirectTrajOpt.jl benchmarks'.
Benchmark result of this commit is worse than the previous benchmark result exceeding threshold 1.20.

Benchmark suite	Current: f29bb9a	Previous: 134c3ac	Ratio
bilinear_N51_ipopt [wall]	1.594580896 s	0.564104588 s	2.83
bilinear_N51_ipopt [alloc]	4318456168 bytes	1432053240 bytes	3.02
bilinear_N51_madnlp [wall]	2.498824858 s	0.363166886 s	6.88
bilinear_N51_madnlp [alloc]	6699092272 bytes	980944936 bytes	6.83
scaling_N101_d4_ipopt [wall]	2.358249771 s	1.054411922 s	2.24
scaling_N101_d4_ipopt [alloc]	6944397408 bytes	2467082832 bytes	2.81
scaling_N25_d16_ipopt [wall]	13.351560731 s	3.044575574 s	4.39
scaling_N25_d16_ipopt [alloc]	51122805800 bytes	5664718144 bytes	9.02
scaling_N25_d8_ipopt [wall]	0.174621301 s	0.012267772 s	14.23
scaling_N25_d8_ipopt [alloc]	644871656 bytes	22826992 bytes	28.25
scaling_N51_d16_ipopt [alloc]	57108354040 bytes	39827022448 bytes	1.43
scaling_N51_d8_ipopt [wall]	2.330262973 s	1.405805628 s	1.66
scaling_N51_d8_ipopt [alloc]	9103164104 bytes	2731535776 bytes	3.33

This comment was automatically generated by workflow using github-action-benchmark.