MTKBaseEnzymeExt: mirror Mooncake's tangent_type=NoTangent via EnzymeRules.inactive_type

[ChrisRackauckas-Claude]

Summary

Adds a new package extension MTKBaseEnzymeExt (triggered on Enzyme) that registers EnzymeRules.inactive_type for the same MTKBase-owned types that MTKMooncakeExt already marks Mooncake.tangent_type = NoTangent. This is one of several follow-ups for full Enzyme support through MTK-generated problem / initialization-problem closures.

Types declared inactive

Type	Where it lives	Rationale
System	lib/ModelingToolkitBase/src/systems/system.jl	Self-referential fields systems::Vector{System}, parent::Union{Nothing, System}, initializesystem::Union{Nothing, System}. Already covered by the existing <:AbstractSystem declaration in ModelingToolkitBase.jl; restated here for one-to-one parity with MTKMooncakeExt and explicitness.
GeneratedFunctionWrapper	lib/ModelingToolkitBase/src/systems/codegen_utils.jl	Wraps RuntimeGeneratedFunctions — the model RHS closure, not a derivative carrier.
ObservedFunctionCache	lib/ModelingToolkitBase/src/systems/abstractsystem.jl	Contains a System reference and a Dict{Any, Any} of cached observed-function closures.
MissingGuessValue.Type	lib/ModelingToolkitBase/src/systems/problem_utils.jl	Moshi @data tagged union (Constant{<:Number} | Random{<:AbstractRNG} | Error) used as a configuration enum for the initialization solver.

Why this is needed

Without these declarations, Enzyme's runtime-activity dispatch and make_zero traversal recurse into self-referential or otherwise-unhandleable fields when a closure (or problem / solution struct) transitively captures one of these values, producing activity-analysis errors or MethodErrors in create_activity_wrapper.

MTKMooncakeExt already handles the equivalent on the Mooncake side via Mooncake.tangent_type(::Type{T}) = NoTangent. This PR brings the Enzyme side to parity for the types MTKBase owns. Types that live in other packages (SciMLBase's OverrideInitData / ODENLStepData, FunctionWrappersWrappers' FunctionWrappersWrapper, Base's ImmutableDict) are intentionally not declared here — they belong in their own packages' Enzyme extensions; separate PRs to follow.

Verification

Local smoke test confirmed the extension loads and the declarations apply:

System inactive: true
GFW{(3,3,true),Nothing,Nothing} inactive: true
ObservedFunctionCache inactive: true
MissingGuessValue.Type inactive: true
MissingGuessValue.Error type inactive: true

Project.toml changes

• Adds Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9" to [weakdeps].
• Adds MTKBaseEnzymeExt = "Enzyme" to [extensions].
• Adds Enzyme = "0.13" to [compat].
• Bumps ModelingToolkitBase patch version to 1.40.1.

Notes

Please ignore until reviewed by @ChrisRackauckas.

This is the second follow-up in a series of small PRs targeting MTKBase's Enzyme story. The first was the <:AbstractSystem inactive_type declaration already on master. A separate PR will address the MTKParameters.canonicalize(::Tunable, ...) repack closure aliasing fresh caches buffers — that fix is independent and stacked on its own branch (enzyme-fresh-caches-on-repack).

Test plan

• CI green on MTKBase tests (no regression from the inactive_type declarations).
• Downstream smoke: SCC init-problem gradient through Enzyme (see test_caches_fix.jl MWE referenced in the surrounding investigation).

Co-Authored-By: Chris Rackauckas accounts@chrisrackauckas.com

[ChrisRackauckas-Claude]

Closing as not required. Ablation study with the desauty SCC init test rewritten to use the proper Enzyme API (Enzyme.autodiff + Duplicated(iprob), SciML/SciMLSensitivity.jl#1454) confirms this PR doesn't change the outcome — desauty still passes with MTKBaseEnzymeExt disabled (file removed and [extensions] entry commented out). The Mooncake-parity inactive_type declarations may still be useful for other Enzyme paths, but I don't have a concrete test that needs them. Can be reopened if one comes up.