Declare fix_dt_at_bounds!, handle_tstop!, initialize_tstops, initialize_saveat, initialize_d_discontinuities public

[ChrisRackauckas]

Declares five OrdinaryDiffEqCore bindings public (not exported) so that packages
building a custom integrator on top of the OrdinaryDiffEqCore machinery can call and
extend them without tripping strict ExplicitImports/SciMLTesting non-public checks.

Unblocks SciML/OrdinaryDiffEqOperatorSplitting.jl#102, which migrates that package to
SciMLTesting 2.4 strict QA. The alternative — rewriting the caller to dodge these
bindings — is not available here: OperatorSplitting adds methods to two of them for
its own integrator type, which is only possible by naming the generic function.

Bindings

Binding	What it is	Downstream use
fix_dt_at_bounds!	Clamps integrator.dt into [dtmin, dtmax] respecting tdir (src/integrators/integrator_utils.jl:894)	OperatorSplitting defines a method (src/utils.jl:164) and calls it (src/integrator.jl:536)
handle_tstop!	Pops/consumes the reached tstop, sets just_hit_tstop, interpolates back for non-dtchangeable algorithms (src/integrators/integrator_utils.jl:909)	OperatorSplitting defines a method (src/integrator.jl:419) and calls it in 3 places; DelayDiffEq calls it in src/solve.jl:584 and src/integrators/interface.jl:695
initialize_tstops	Builds the internal BinaryHeap of tdir-signed tstops from user tstops/d_discontinuities/tspan (src/solve.jl:978)	Called by OperatorSplitting (src/integrator.jl:233, :1020) and DelayDiffEq (src/solve.jl:277, src/integrators/interface.jl:436)
initialize_saveat	Builds the internal saveat heap from the user saveat keyword (src/solve.jl:1030)	Called by OperatorSplitting (src/integrator.jl:236) and DelayDiffEq (src/solve.jl:281, src/integrators/interface.jl:440)
initialize_d_discontinuities	Builds the internal d_discontinuities heap (src/solve.jl:1075)	Called by OperatorSplitting (src/integrator.jl:237) and DelayDiffEq (src/solve.jl:282, src/integrators/interface.jl:441)

Why interface, not implementation detail

• fix_dt_at_bounds! and handle_tstop! are generic functions that downstream integrator
  packages are expected to extend — a generic function with downstream methods is an
  extension point by definition, and both existing custom-integrator consumers in the
  ecosystem (DelayDiffEq in this repo, OperatorSplitting out of tree) do exactly that.
• handle_tstop! is already documented as part of the main solver loop in
  docs/src/devtools/contributing/diffeq_internals.md.
• The three initialize_* functions are the only supported way to construct the internal
  heap representations that DEOptions requires. DEOptions is already public; a public
  struct whose fields cannot be constructed with public API is not usable.
• lib/DelayDiffEq/test/qa/qa_tests.jl already carries all five (well, four of them, plus a
  larger set) on its non-public ignore list with the comment "make-public candidates" — this
  PR resolves that subset in the owning package rather than in each caller.

Already public — deliberately not touched

stepsize_controller!, step_accept_controller! and step_reject_controller! were also
flagged upstream, but they are already declared public in
lib/OrdinaryDiffEqCore/src/OrdinaryDiffEqCore.jl (the controller-author block at the top,
and again in the solver-author block). No change needed; declaring them again would be noise.

Style

Matches the file's existing @static if VERSION >= v"1.11.0-DEV.469" /
eval(Expr(:public, ...)) pattern, which keeps the Julia 1.10 floor parsing. This repo does
not use SciMLPublic, so no new dependency was added.

Verification

julia --project=lib/OrdinaryDiffEqCore -e 'using OrdinaryDiffEqCore'   # succeeds
length(names(OrdinaryDiffEqCore))  # 369 before -> 374 after (+5, no losses)

All five confirmed non-public before the edit and public after. Runic clean. Minor version
bump 4.12.0 -> 4.13.0 so downstream can set a compat bound that guarantees the declarations.

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