Fix MIRK constrained interpolation without controls

[ChrisRackauckas-Claude]

This PR should be ignored until reviewed by @ChrisRackauckas.

Summary

• Distinguish true control-variable BVPs from constrained pure-state BVPs in MIRK interpolation.
• Keep linear interpolation only for solution entries beyond f_prototype, instead of treating every non-nothing f_prototype as controls.
• Add a regression test for the issue Interpolation bug in MIRK4 solutions to constrained BVP #533 constrained MIRK4 + Ipopt interpolation case with no cost function.

Verification

• Reproduced issue Interpolation bug in MIRK4 solutions to constrained BVP #533 locally on current master: solve returned Success, then sol(0.5) threw ArgumentError: range must be non-empty from BoundaryValueDiffEqMIRK/src/interpolation.jl:116.
• Ran the patched MRE in a temporary Julia environment developing this checkout: solve returned Success; sol(0.5) = [0.4434094419864602, -0.9595173756818917].
• Ran Runic.jl formatting on the two touched files via a temporary local environment.
• Ran git diff --check: passed.
• Ran timeout 3600 julia --project=lib/BoundaryValueDiffEqMIRK -e 'using Pkg; Pkg.test()': failed/timed out after one hour. Before timeout, existing MIRK basic tests reported MethodError: no method matching Float64(::ForwardDiff.Dual...) in Swirling Flow III, Test interpolant evaluation with big defect, and Test maxsol and minsol; then the suite continued through many Ipopt solves until timeout. A separate agent is investigating whether that reproduces on clean master.

[github-actions]

Benchmark Results (Julia v1.11)

Time benchmarks

	master	867eaa8...	master / 867eaa8...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2()	0.581 ± 0.0098 s	0.573 ± 0.01 s	1.01 ± 0.025
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3()	12.1 ± 0.15 ms	12 ± 0.19 ms	1.01 ± 0.021
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4()	2.66 ± 0.063 ms	2.63 ± 0.078 ms	1.01 ± 0.038
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5()	3.23 ± 0.11 ms	3.16 ± 0.098 ms	1.02 ± 0.046
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6()	1.55 ± 0.044 ms	1.54 ± 0.047 ms	1.01 ± 0.042
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.49 ± 0.071 ms	1.49 ± 0.062 ms	1 ± 0.064
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	3.2 ± 0.15 ms	3.14 ± 0.21 ms	1.02 ± 0.083
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0405 ± 0.0032 s	0.0387 ± 0.0028 s	1.05 ± 0.11
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.0611 ± 0.0017 s	0.0587 ± 0.0015 s	1.04 ± 0.04
Simple Pendulum/IIP/Shooting(Tsit5())	0.173 ± 0.072 ms	0.174 ± 0.072 ms	0.996 ± 0.58
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2()	2.23 ± 0.013 s	0.715 ± 0.0046 s	3.12 ± 0.027
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3()	31.3 ± 5.1 ms	15.4 ± 4.8 ms	2.03 ± 0.71
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4()	4.79 ± 0.14 ms	3.19 ± 0.12 ms	1.5 ± 0.069
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5()	5.74 ± 0.21 ms	3.79 ± 0.18 ms	1.52 ± 0.09
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6()	2.46 ± 0.1 ms	1.83 ± 0.093 ms	1.34 ± 0.089
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	3.28 ± 0.78 ms	3.2 ± 0.33 ms	1.02 ± 0.27
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	6.44 ± 5.4 ms	6.51 ± 5.4 ms	0.988 ± 1.2
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.091 ± 0.0039 s	0.0813 ± 0.0027 s	1.12 ± 0.061
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.135 ± 0.0054 s	0.125 ± 0.0027 s	1.08 ± 0.049
Simple Pendulum/OOP/Shooting(Tsit5())	0.596 ± 0.032 ms	0.597 ± 0.039 ms	0.998 ± 0.085
time_to_load	7.07 ± 0.038 s	7.04 ± 0.013 s	1 ± 0.0056

Memory benchmarks

	master	867eaa8...	master / 867eaa8...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2()	0.389 M allocs: 0.0443 GB	0.389 M allocs: 0.0443 GB	1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3()	0.0436 M allocs: 4.88 MB	0.0436 M allocs: 4.88 MB	1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4()	15.7 k allocs: 1.65 MB	15.7 k allocs: 1.65 MB	1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5()	22.1 k allocs: 2.03 MB	22.1 k allocs: 2.03 MB	1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6()	12.8 k allocs: 1.05 MB	12.8 k allocs: 1.05 MB	1
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	25.5 k allocs: 1.82 MB	25.5 k allocs: 1.82 MB	1
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	0.0491 M allocs: 3.39 MB	0.0491 M allocs: 3.39 MB	1
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.553 M allocs: 0.0535 GB	0.553 M allocs: 0.0535 GB	1
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.833 M allocs: 0.0778 GB	0.833 M allocs: 0.0778 GB	1
Simple Pendulum/IIP/Shooting(Tsit5())	4.63 k allocs: 0.224 MB	4.63 k allocs: 0.224 MB	1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2()	0.89 M allocs: 0.984 GB	0.89 M allocs: 0.984 GB	1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3()	0.0932 M allocs: 24.8 MB	0.0932 M allocs: 24.8 MB	1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4()	0.0324 M allocs: 3.96 MB	0.0324 M allocs: 3.96 MB	1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5()	0.045 M allocs: 4.99 MB	0.045 M allocs: 4.99 MB	1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6()	25.3 k allocs: 2.17 MB	25.3 k allocs: 2.17 MB	1
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	0.142 M allocs: 10.2 MB	0.142 M allocs: 10.2 MB	1
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	0.266 M allocs: 18.7 MB	0.266 M allocs: 18.7 MB	1
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	2.52 M allocs: 0.279 GB	2.52 M allocs: 0.279 GB	1
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	3.82 M allocs: 0.404 GB	3.82 M allocs: 0.404 GB	1
Simple Pendulum/OOP/Shooting(Tsit5())	0.0373 M allocs: 1.69 MB	0.0373 M allocs: 1.69 MB	1
time_to_load	0.159 k allocs: 11.2 kB	0.159 k allocs: 11.2 kB	1