Document direct operator-splitting developer interfaces

[ChrisRackauckas-Claude]

Summary

• move developer-interface docstrings to their original generic definitions
• split user-facing and solver-developer guidance, including extension rules and generic examples
• add a test-only external operator-splitting solver that uses only the documented generic interfaces
• reduce the strict-QA exception list to the names that genuinely have no public spelling

Strict QA

The bare run_qa(OrdinaryDiffEqOperatorSplitting) failed on five names, not one. They fall into two groups.

Fixed by accessing the owner. dotview and broadcastable are public in Base.Broadcast but not in Base, and src/config_tree.jl reached them through Base. All four broadcast overloads now qualify through Base.Broadcast, which drops both findings with no exception entry.

Genuinely non-public, so allowed. On Julia 1.12.6:

name	Base	Base.Broadcast
dotview	✗	✓
broadcastable	✗	✓
BroadcastStyle	✗	✓
materialize!	✗	✗
Broadcasted	✗	✗

materialize! and Broadcasted have no public spelling in either module and no alias, so an empty exception list is unreachable while TreeOption implements .=. They are allowed with the reason inline in test/qa/qa.jl. failfactor_default joins them until a registered OrdinaryDiffEqCore carries SciML/OrdinaryDiffEq.jl#4111 — that one is temporary.

Note that SciMLTesting #43/#44 do not affect any of this; they change the Aqua subprocess load path and the persistent_tasks allowance.

Verification

• GROUP=Core Pkg.test() on Julia 1.12.6 — all groups pass (adaptivity 70, alias_u0 13, backward 35, callbacks 77, config_tree 140, consistency 27, convergence 90, failure_escalation 20, operator_splitting_api 1342, saving 122, sync 9)
• test/qa/qa.jl on Julia 1.12.6 (21/21) and 1.10.11 LTS (19/19)
• strict docs build on Julia 1.12
• Runic clean on src, test, docs

Dependencies

• a registered OrdinaryDiffEqCore release containing Make failfactor_default and qmax_first_step_default public OrdinaryDiffEq.jl#4111, to drop the failfactor_default entry

Ignore until reviewed by @ChrisRackauckas.

[termi-official]

No. This should be done with the new interface (set_EEst or so) which we recently added to OrdinaryDiffEqCore.

[ChrisRackauckas-Claude]

Done in 050a1fb — the guidance, the code block, and the _perform_step! docstring now go through OrdinaryDiffEqCore.set_EEst!, with a note that it and get_EEst are the interface and the field location is an implementation detail.

Worth flagging that the package was already inconsistent with itself here: src/integrator.jl defines OrdinaryDiffEqCore.set_EEst!/get_EEst for the split integrator types and the controllers read the estimate through them, but the built-in PalindromicPairLieTrotterGodunov still assigned the field directly. Since the docs cite it as the complete example, I changed it too, plus a stale comment in integrator.jl describing the estimate as "written to the node's EEst".

I left the two direct writes in reinit_node_controller! alone — those are the implementation side of the hook writing the package's own field, so routing them through set_EEst! would just call back into the same assignment. Say the word if you'd rather they were uniform.

Verified locally on Julia 1.12.6: full Core group passes (adaptivity 70/70 covers the PPLTG estimate path), strict docs build exit 0, Runic clean.