Add DifferentiationInterface.Prep support to anyeltypedual

This commit adds support for DifferentiationInterface.Prep types
to opt out of dual number checking. This fixes issue #718 in
NonlinearSolve.jl where Prep objects in parameters were incorrectly
triggering automatic differentiation detection.

Changes:
- Added DifferentiationInterface to weakdeps and extensions in Project.toml
- Created new extension SciMLBaseDifferentiationInterfaceExt with
  anyeltypedual overloads for Prep types, following the same pattern
  as ForwardDiff.AbstractConfig

Fixes SciML/NonlinearSolve.jl#718

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

Project.toml

@@ -37,6 +37,7 @@ SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
 [weakdeps]
 ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -55,6 +56,7 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [extensions]
 SciMLBaseChainRulesCoreExt = "ChainRulesCore"
+SciMLBaseDifferentiationInterfaceExt = "DifferentiationInterface"
 SciMLBaseDistributionsExt = "Distributions"
 SciMLBaseEnzymeExt = "Enzyme"
 SciMLBaseForwardDiffExt = "ForwardDiff"
@@ -80,6 +82,7 @@ ChainRules = "1.58.0"
 ChainRulesCore = "1.18"
 CommonSolve = "0.2.4"
 ConstructionBase = "1.5"
+DifferentiationInterface = "0.6, 0.7"
 Distributed = "1.10"
 Distributions = "0.25"
 DocStringExtensions = "0.9"

ext/SciMLBaseDifferentiationInterfaceExt.jl

@@ -0,0 +1,18 @@
+module SciMLBaseDifferentiationInterfaceExt
+
+using SciMLBase, DifferentiationInterface
+
+import SciMLBase: anyeltypedual
+
+# Opt out since these are using for preallocation, not differentiation
+function anyeltypedual(x::DifferentiationInterface.Prep,
+        ::Type{Val{counter}} = Val{0}) where {counter}
+    Any
+end
+function anyeltypedual(x::Type{T},
+        ::Type{Val{counter}} = Val{0}) where {counter} where {T <:
+                                                              DifferentiationInterface.Prep}
+    Any
+end
+
+end