Use SciMLTesting public API docs QA

[ChrisRackauckas-Claude]

Ignore this PR until reviewed by @ChrisRackauckas.

Summary

• Update BoundaryValueDiffEq QA/docs coverage to use SciMLTesting v2.1 public API documentation checks.
• Remove package self [sources] path entries while preserving required monorepo sibling sources.
• Add rendered API docs coverage for the package docs.

Validation

• timeout 3600 julia --project=. -e 'using Pkg; ENV["GROUP"] = "QA"; Pkg.test(; allow_reresolve = true)' passed.
• Subpackage QA loop passed for Core, Ascher, MIRKN, Shooting, MIRK, FIRK.
• timeout 3600 julia --project=. -e 'using Pkg; ENV["GROUP"] = "Wrappers"; Pkg.test(; allow_reresolve = true)' passed.
• FIRK AD and MIRK AD loop passed.
• TOML parse over all Project.toml files passed.
• git diff --check passed.
• Runic check on changed Julia files passed.
• api_docs = false scan returned no matches.
• Parsed self-source scan returned no self-source entries.

[github-actions]

Benchmark Results (Julia v1.11)

Time benchmarks

	master	3faf56e...	master / 3faf56e...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2()	0.58 ± 0.008 s	0.574 ± 0.009 s	1.01 ± 0.021
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3()	12.1 ± 0.15 ms	12 ± 0.17 ms	1 ± 0.019
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4()	2.65 ± 0.058 ms	2.62 ± 0.053 ms	1.01 ± 0.03
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5()	3.19 ± 0.091 ms	3.15 ± 0.1 ms	1.01 ± 0.044
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6()	1.54 ± 0.031 ms	1.52 ± 0.037 ms	1.01 ± 0.032
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.48 ± 0.048 ms	1.47 ± 0.054 ms	1 ± 0.049
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	3.09 ± 0.089 ms	3.05 ± 0.096 ms	1.01 ± 0.043
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0381 ± 0.0026 s	0.0381 ± 0.0026 s	0.999 ± 0.095
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.0581 ± 0.00087 s	0.0578 ± 0.0011 s	1 ± 0.024
Simple Pendulum/IIP/Shooting(Tsit5())	0.174 ± 0.072 ms	0.171 ± 0.072 ms	1.02 ± 0.6
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2()	0.712 ± 0.0037 s	0.706 ± 0.0091 s	1.01 ± 0.014
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3()	15.3 ± 4 ms	15.1 ± 3.8 ms	1.02 ± 0.37
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4()	3.19 ± 0.12 ms	3.16 ± 0.13 ms	1.01 ± 0.056
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5()	3.8 ± 0.19 ms	3.81 ± 0.19 ms	0.997 ± 0.069
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6()	1.83 ± 0.087 ms	1.82 ± 0.1 ms	1 ± 0.074
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	3.2 ± 0.35 ms	3.22 ± 0.39 ms	0.995 ± 0.16
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	6.2 ± 4.9 ms	6.19 ± 5 ms	1 ± 1.1
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0815 ± 0.0027 s	0.0808 ± 0.0018 s	1.01 ± 0.04
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.125 ± 0.003 s	0.126 ± 0.0042 s	0.995 ± 0.041
Simple Pendulum/OOP/Shooting(Tsit5())	0.598 ± 0.034 ms	0.59 ± 0.037 ms	1.01 ± 0.085
time_to_load	7.26 ± 0.034 s	7.28 ± 0.019 s	0.996 ± 0.0054

Memory benchmarks

	master	3faf56e...	master / 3faf56e...
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)	0.049 M allocs: 3.39 MB	0.049 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