fix: DynamicQuantities compatibility in core + differentiation paths

[MilesCranmerBot]

Wave 2 (post-DynamicQuantities release) for the DynamicQuantities × SciML rollout.
Tracking issue: JuliaPhysics/DynamicQuantities.jl#200

What this changes

OrdinaryDiffEqCore

• Adds DynamicQuantities + Measurements integration test (lib/OrdinaryDiffEqCore/test/dynamicquantities_measurements.jl)
• Uses a unitless bottom-eltype path in solver init to avoid zero(::Type{<:Quantity}) on runtime-unit quantity types
• Includes related unit-safe initialization/caching updates used by this path

OrdinaryDiffEqDifferentiation

• Makes unitful Jacobian derivative utilities robust for DynamicQuantities value-space factorization/solve
• Removes silent AD backend fallback behavior

Notes

• This is expected to be meaningful once DynamicQuantities release with the new extensions is available.
• Related DiffEqBase PR: fix: add DynamicQuantities extension for unitful factorization paths DiffEqBase.jl#1293

Local testing

• julia --project=lib/OrdinaryDiffEqCore -e 'using Pkg; Pkg.test()'
  • current failure before DQ tag: test uses registered DynamicQuantities lacking required runtime-unit fixes (zero(::Type{<:Quantity}) path).

[ChrisRackauckas]

Rebase and add the lower bound

[MilesCranmer]

@MilesCranmerBot please see comment above^ - can you rebase and add lower bound

[MilesCranmerBot]

Done — rebased onto current master and added a lower bound for DynamicQuantities.

• Rebased branch: wave2-odecore
• Lower bound change: DynamicQuantities = "1.8" in lib/OrdinaryDiffEqCore/Project.toml
• Commit: ffed533

I also ran Pkg.test() for OrdinaryDiffEqCore; it currently errors in the new DynamicQuantities+Measurements test due to eps(::DynamicQuantities.Quantity) during init dt.

[ChrisRackauckas]

There are some CI failures to look at.