Make _process_verbose_param(::Bool) constprop-friendly to fix @inferred solve

[ChrisRackauckas-Claude]

Depends on #3365 — this branch is move_verbosity + one extra commit. Once #3365 merges, only the new commit (Make _process_verbose_param(::Bool) constprop-friendly) will remain on the diff against master. If preferred, this can be merged into #3365's branch first; mirror PR was at jClugstor#2 (closed in favor of this).

Summary

• DEFAULT_VERBOSE and NONE_VERBOSE are different concrete parameterizations of DEVerbosity{...} (different Silent/WarnLevel/InfoLevel type parameters per toggle), so the ternary verbose ? DEFAULT_VERBOSE : NONE_VERBOSE returns a Union{...} whenever verbose::Bool isn't a compile-time constant.
• That Union flows into the solver caches — you can see LinearVerbosity{Silent,Silent,...,WarnLevel,WarnLevel,...} baked into the LinearCache type in Move DEVerbosity and default verbosity to DiffEqBase #3365's CI failure logs — and it poisons return-type inference all the way to ODESolution. Tests like @inferred solve(prob_mm, Rodas5P(), ...) in lib/OrdinaryDiffEqRosenbrock/test/dae_rosenbrock_ad_tests.jl fail with does not match inferred return type Any.
• This PR annotates the Bool method with Base.@constprop :aggressive so the compiler threads the literal default verbose = true through the kwargs chain to a single concrete DEVerbosity parameterization.
• Adds Val{true}/Val{false} overloads as an explicit type-stable entry point for callers that don't want to rely on constprop reaching them.

The runtime-Bool-with-no-constprop case still returns a Union; that's an inherent property of the @verbosity_specifier design (verbosity levels are encoded as type parameters). The proper fix for that case is to keep verbosity out of the cache type parameters, but this is the smallest change that unblocks #3365's @inferred tests.

Test plan

• New lib/DiffEqBase/test/verbose_inference.jl exercises both the Val-dispatch path (unconditionally inferable) and the literal-Bool constprop path (verifies Base.return_types resolves to a single concrete type).
• Runic clean.
• Re-run the Rosenbrock / DiffEqDevTools / Integrators test groups that were failing on Move DEVerbosity and default verbosity to DiffEqBase #3365 with @inferred solve(...) errors.

[jClugstor]

Testing the MWE in #3351 with this change, I still get that the inferred return type is Any.

Putting a function barrier like :

_verbose = verbose isa Bool ? (verbose ? Standard() : None()) : verbose
    return _ode_init(prob, alg, timeseries_init, ts_init, ks_init; verbose = _verbose, kwargs...)

in OrdinaryDiffEqCore.__init doesn't let @inferred pass, but it makes the inference better, it infers as a Union of the two possible verbosity objects from the Bool path.

I haven't found a way to make the Bool path fully infer yet.

[ChrisRackauckas]

This at least makes constant prop work which I think is good enough for the pre-v7 if verbosity is fully supported downstream, because then the defaults and the suggested ways to set verbose are all covered.