Enforce repository-wide strict API documentation QA

[ChrisRackauckas-Claude]

Ignore until reviewed by @ChrisRackauckas.

Summary

• document every package-owned public API at its definition and render it in the manual
• exercise the documented matrix-free interfaces through external-call tests
• run standard SciMLTesting 2.4 QA without package-specific public/import exceptions, including the StaticArrays extension
• replace uses of dependency internals with owner APIs or local package-specific helpers
• remove accidental/internal exports and dead StegrWork implementation

The allocation-free matrix-balancing helper is a local implementation because the stdlib LAPACK wrapper used previously is not public and the hot path's zero-allocation contract must be preserved. The new tests compare it with GenericSchur.balance! across real/complex Float32/Float64 inputs and check zero allocations.

This is separate from #266, which promotes and documents alloc_mem.

Local verification

• julia +release --project=. -e 'using Pkg; Pkg.test()': passed (770 tests; 1 pre-existing broken AllocCheck assertion)
• julia +1.10 --project=. -e 'using Pkg; Pkg.test()': passed (770 tests; same pre-existing broken assertion)
• release QA: passed (21/21 package QA checks; 6/6 extension checks)
• Julia 1.10 QA: passed (19/19 package QA checks; 4/4 extension checks)
• release docs build: passed
• Julia 1.10 docs build: passed
• Runic check: passed

GPU tests were not run locally because this machine has no available NVIDIA device.

[ChrisRackauckas-Claude]

Follow-up commit 10cdf65 fixes the observed CUDA scalar-indexing failure by materializing the CPU reduced-space view before copying it into GPU storage. It also adds a focused public expv CUDA regression test.

Local validation after the change:

• Julia 1.12.6 Pkg.test(): 770 passed, 1 unchanged broken
• Julia 1.10.11 Pkg.test(): 770 passed, 1 unchanged broken
• plain strict QA: 28 passed, 2 unchanged broken
• 100,000 deterministic static-matrix Jacobian seeds: passed
• Runic and git diff --check: passed

The CUDA suite cannot run locally because this host has no NVIDIA device; the refreshed real-GPU CI job is authoritative. The unrelated Windows failure is an unchanged unseeded static-Jacobian test and was not altered in this docs/QA PR.