Fix QA public API docs paths

[ChrisRackauckas-Claude]

This PR should be ignored until reviewed by @ChrisRackauckas.

Summary

• Anchor the public API docs QA source paths to the repository root.
• Anchor docs entry discovery to the repository root instead of the QA test process working directory.

Root Cause

The QA group runs from the test/qa environment, so relative paths like src and docs/src can resolve under test/qa instead of the repository root. That makes the public API docs coverage check fail in CI.

Verification

• timeout 3600 env TMPDIR=/home/crackauc/sandbox/tmp_20260708_121627_10236/tmp JULIA_DEPOT_PATH=/home/crackauc/sandbox/tmp_20260708_121627_10236/julia_depot_bvd_qa_current GROUP=QA julia +1 --startup-file=no --project=. -e 'import Pkg; Pkg.test(; coverage=false, julia_args=["--check-bounds=yes", "--compiled-modules=yes", "--depwarn=yes"], force_latest_compatible_version=false, allow_reresolve=true)'\n - Quality Assurance | 173 pass\n - Testing BoundaryValueDiffEq tests passed\n- git diff --check origin/master..HEAD\n- timeout 3600 julia +1 --startup-file=no --project=/home/crackauc/sandbox/tmp_20260708_121627_10236/runic_env -e 'using Runic; exit(Runic.main(["--check", "--verbose", "."]))'\n\n## Notes\n- This only addresses the root CI QA path failure. MIRK/Shooting downgrade, docs, ModelingToolkit downstream, and FIRK EXPANDED failures are separate master failures.

[github-actions]

Benchmark Results (Julia v1.11)

Time benchmarks

	master	d22e2bd...	master / d22e2bd...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2()	0.581 ± 0.008 s	0.58 ± 0.015 s	1 ± 0.029
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3()	12.1 ± 0.19 ms	12 ± 0.17 ms	1.01 ± 0.021
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4()	2.65 ± 0.056 ms	2.62 ± 0.062 ms	1.01 ± 0.032
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5()	3.18 ± 0.084 ms	3.2 ± 0.077 ms	0.996 ± 0.035
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6()	1.53 ± 0.037 ms	1.52 ± 0.035 ms	1 ± 0.034
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.5 ± 0.057 ms	1.51 ± 0.071 ms	0.994 ± 0.06
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	3.09 ± 0.13 ms	3.1 ± 0.11 ms	0.997 ± 0.054
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0379 ± 0.0024 s	0.0379 ± 0.0028 s	1 ± 0.096
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.0578 ± 0.0015 s	0.0587 ± 0.0013 s	0.985 ± 0.034
Simple Pendulum/IIP/Shooting(Tsit5())	0.171 ± 0.069 ms	0.173 ± 0.071 ms	0.992 ± 0.57
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2()	0.711 ± 0.014 s	0.726 ± 0.0029 s	0.978 ± 0.019
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3()	15.5 ± 4.2 ms	15.4 ± 4.7 ms	1.01 ± 0.41
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4()	3.14 ± 0.12 ms	3.15 ± 0.14 ms	0.998 ± 0.059
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5()	3.85 ± 0.2 ms	3.76 ± 0.21 ms	1.02 ± 0.078
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6()	1.84 ± 0.073 ms	1.82 ± 0.1 ms	1.01 ± 0.069
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	3.22 ± 0.5 ms	3.33 ± 0.49 ms	0.968 ± 0.21
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	6.24 ± 4.9 ms	6.43 ± 5.7 ms	0.97 ± 1.1
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0813 ± 0.0027 s	0.0854 ± 0.0073 s	0.952 ± 0.088
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.128 ± 0.0052 s	0.128 ± 0.0047 s	1 ± 0.055
Simple Pendulum/OOP/Shooting(Tsit5())	0.597 ± 0.03 ms	0.611 ± 0.03 ms	0.978 ± 0.068
time_to_load	6.97 ± 0.032 s	6.96 ± 0.068 s	1 ± 0.011

Memory benchmarks

	master	d22e2bd...	master / d22e2bd...
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