Fix Enzyme solve_up rule signature to support DuplicatedNoNeed

Fixes SciML/SciMLSensitivity.jl#1225

The Enzyme rules for solve_up were failing when sensealg was passed
via the ODEProblem constructor instead of solve(). The issue was that
the return type annotation was restricted to Duplicated{RT}, but Enzyme
can also use DuplicatedNoNeed{RT}.

Changes:
- Updated augmented_primal signature to accept both Duplicated and DuplicatedNoNeed
- Updated reverse signature to accept both Duplicated and DuplicatedNoNeed
- Fixed type handling to extract the inner result type instead of using the annotation type
- Removed incorrect type assertion in reverse function

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

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

Author: ChrisRackauckas

ext/DiffEqBaseEnzymeExt.jl

@@ -9,10 +9,10 @@ module DiffEqBaseEnzymeExt
 
     function Enzyme.EnzymeRules.augmented_primal(
             config::Enzyme.EnzymeRules.RevConfigWidth{1},
-            func::Const{typeof(DiffEqBase.solve_up)}, ::Type{Duplicated{RT}}, prob,
+            func::Const{typeof(DiffEqBase.solve_up)}, ::Type{RT}, prob,
             sensealg::Union{
                 Const{Nothing}, Const{<:DiffEqBase.AbstractSensitivityAlgorithm}},
-            u0, p, args...; kwargs...) where {RT}
+            u0, p, args...; kwargs...) where {RT <: Union{Duplicated, DuplicatedNoNeed}}
         @inline function copy_or_reuse(val, idx)
             if Enzyme.EnzymeRules.overwritten(config)[idx] && ismutable(val)
                 return deepcopy(val)
@@ -31,18 +31,18 @@ module DiffEqBaseEnzymeExt
             SciMLBase.EnzymeOriginator(), ntuple(arg_copy, Val(length(args)))...;
             kwargs...)
 
-        dres = Enzyme.make_zero(res[1])::RT
+        ResType = typeof(res[1])
+        dres = Enzyme.make_zero(res[1])::ResType
         tup = (dres, res[2])
-        return Enzyme.EnzymeRules.AugmentedReturn{RT, RT, Any}(res[1], dres, tup::Any)
+        return Enzyme.EnzymeRules.AugmentedReturn{ResType, ResType, Any}(res[1], dres, tup::Any)
     end
 
     function Enzyme.EnzymeRules.reverse(config::Enzyme.EnzymeRules.RevConfigWidth{1},
-            func::Const{typeof(DiffEqBase.solve_up)}, ::Type{Duplicated{RT}}, tape, prob,
+            func::Const{typeof(DiffEqBase.solve_up)}, ::Type{RT}, tape, prob,
             sensealg::Union{
                 Const{Nothing}, Const{<:DiffEqBase.AbstractSensitivityAlgorithm}},
-            u0, p, args...; kwargs...) where {RT}
+            u0, p, args...; kwargs...) where {RT <: Union{Duplicated, DuplicatedNoNeed}}
         dres, clos = tape
-        dres = dres::RT
         dargs = clos(dres)
         for (darg, ptr) in zip(dargs, (func, prob, sensealg, u0, p, args...))
             if ptr isa Enzyme.Const