Fix Zygote gradient through scaled concretization

[AshtonSBradley]

Summary

• Fixes a Zygote sensitivity bug where update_coefficients(...) |> concretize for a scaled operator could produce a doubled gradient compared with the equivalent matrix expression.
• Keeps ScaledOperator immutable, addressing the allocation concern from review.
• Freezes updated ScalarOperator state into a private immutable scalar snapshot for the out-of-place scaled update path.
• Adds AD semantic equivalence tests for scaled and added matrix operators across concretization, direct application, and mutating application.
• Bumps the ArrayInterface lower bound so downgrade CI resolves a test-compatible Adapt version with ALLOW_RERESOLVE=false.

Fixes #305.

Explanation

Issue #305 reduces to a small operator expression of the form MatrixOperator(A1) + ScalarOperator(...) * MatrixOperator(A2). The primal value from update_coefficients(...) |> concretize matches the equivalent dense matrix expression, but Zygote sees an extra sensitivity contribution through the scaled-operator update path and returns a doubled gradient.

The first version of this PR avoided that by making ScaledOperator mutable, but review correctly pointed out that this is allocation-sensitive and not the right tradeoff. The revised fix keeps ScaledOperator immutable. Instead, after the scalar coefficient has been updated out-of-place, the updated ScalarOperator is converted to a private immutable _UpdatedScalarOperator snapshot before reconstructing the ScaledOperator.

That preserves the existing mutable ScalarOperator behavior for normal in-place coefficient updates while giving Zygote an immutable scalar value in the out-of-place path that is used by concretization. The in-place update_coefficients!(::ScaledOperator, ...) behavior is left unchanged, and this does not add new public API or dependencies.

The downgrade CI failure was a resolver conflict before tests ran: the root lower-bound environment selected Adapt v4.0.0, while the test dependency stack required compatibility with Adapt v4.5.2-4. Raising the package lower bound to ArrayInterface = "7.24" makes the downgraded root environment select an Adapt version compatible with the tests while keeping the downgrade check meaningful.

Tests

• Focused Wrong result when Zygote differentiate through update_coefficient and concretize #305 reproducer comparing the operator and matrix gradients: operator and matrix gradients both evaluate to 1.0.
• Focused Zygote and AD semantic test run:
  • julia --project=test -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate(); using Test; include("test/zygote.jl"); include("test/ad_semantics.jl")'
  • Zygote update_coefficients concretize scaled operator | 2 passed
  • AD semantic equivalence | 10 passed
• Format check:
  • julia --project=@runic -e 'using Runic; exit(Runic.main(ARGS))' -- --check src/basic.jl src/scalar.jl test/runtests.jl test/ad_semantics.jl Project.toml
• Full package tests:
  • julia --project=. -e 'using Pkg; Pkg.test()'
  • SciMLOperators | 896 passed, 2 broken, 898 total
• Downgrade CI reproduction on Julia 1.10:
  • julia +1.10 --project=. -e 'import Pkg; Pkg.test(; coverage=true, julia_args=["--check-bounds=yes", "--compiled-modules=yes", "--depwarn=yes"], force_latest_compatible_version=false, allow_reresolve=false)'
  • SciMLOperators | 896 passed, 2 broken, 898 total

[ChrisRackauckas]

this will cause some allocations, seems like not the right solution.

[AshtonSBradley]

I hope this is getting closer