Complete public callback API documentation

[ChrisRackauckas-Claude]

Ignore until reviewed by @ChrisRackauckas.

Summary

• complete SciMLStyle definition-site documentation for all 22 owned exported names, including exact calling forms, arguments, keywords, return contracts, failure modes, and runnable examples
• correct inaccurate public documentation for domain, manifold, integrating, saving, probabilistic, and termination callbacks without changing runtime behavior or exports
• document the generic iteration contract of IndependentlyLinearizedSolution and add focused tests for its yielded (t, values) shape and contents

Audit process

• inspected the current open pull requests and synced from SciML/DiffEqCallbacks.jl master before creating the feature branch
• ran clean-base release and Julia 1.10 package and strict-QA tests before editing
• audited every owned export for definition-site documentation and rendered @docs coverage; all 22 are attached and rendered
• kept the change to docstrings plus one interface-contract test; no source-path metadata, blanket reexports, QA suppressions, or test disabling were added
• retained SciMLTesting = "2.4" compatibility in both test environments

Local validation

• Runic --check .: exit 0, no output
• git diff --check: exit 0, no output
• Julia 1.12.6 / release Pkg.test(): all callback groups passed; Testing DiffEqCallbacks tests passed
• Julia 1.12.6 / release GROUP=QA Pkg.test(): QA/jet_tests.jl 15/15 and QA/qa.jl 22/22; passed
• Julia 1.10.11 Pkg.test(): all callback groups passed; Testing DiffEqCallbacks tests passed
• Julia 1.10.11 GROUP=QA Pkg.test(): existing LTS JET marker Broken 1/1, QA/qa.jl 20/20; passed
• Documenter build on Julia 1.12.6: exit 0 after retrying the initial one-hour HTML serialization timeout with a two-hour timeout; doctests, cross-references, document checks, and HTML rendering completed

[ChrisRackauckas-Claude]

The only failing check is the downgrade Core job: https://github.com/SciML/DiffEqCallbacks.jl/actions/runs/31045683568/job/92440495994

The downgraded environment resolves OrdinaryDiffEqRosenbrock to a release that imports and calls OrdinaryDiffEqCore.namify; the selected Core release does not provide that binding, so Rosenbrock fails to precompile before domain_tests.jl. This PR changes callback definition-site docstrings and one independently-linearized callback test, with no Project or compatibility change. I am keeping the dependency-resolution failure separate rather than changing callback code or weakening the downgrade job. A clean-default-branch downgrade reproduction is still required before this draft is marked ready.

Ignore this draft until reviewed by @ChrisRackauckas.

[ChrisRackauckas-Claude]

CI follow-up:

• Documentation, Runic, spelling, AD, Core, QA, and all Julia/platform matrix jobs passed.
• The sole failing check is the pre-existing Core Downgrade failure also present on current master. Both runs resolve OrdinaryDiffEqRosenbrock v1.8.0 with OrdinaryDiffEqCore v1.32.0, then fail because namify is unavailable.
• Reproduced that exact pair locally on Julia 1.10.11; OrdinaryDiffEqRosenbrock v1.18.1 loads successfully with the same Core version.
• Tracked separately in Downgrade CI resolves incompatible OrdinaryDiffEqRosenbrock/Core versions #334 so this documentation PR remains focused.