Use SciMLBase.set_mooncakeoriginator_if_mooncake for Mooncake AD support

NonlinearSolveBase was passing `SciMLBase.ChainRulesOriginator()` directly without
wrapping it in `set_mooncakeoriginator_if_mooncake`. This caused the `originator`
to remain as `ChainRulesOriginator` when using Mooncake AD, instead of being
converted to `MooncakeOriginator`.

This fix:
- Removes the unused local `set_mooncakeoriginator_if_mooncake` definition from utils.jl
- Updates solve.jl to wrap originator with `SciMLBase.set_mooncakeoriginator_if_mooncake`

This enables proper Mooncake AD support detection in downstream packages like
SciMLSensitivity.

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

Co-Authored-By: Claude Opus 4.5 <[email protected]>

Author: ChrisRackauckas

lib/NonlinearSolveBase/src/solve.jl

@@ -90,7 +90,7 @@ function solve(prob::AbstractNonlinearProblem, args...; sensealg = nothing,
             p,
             args...;
             alias = alias_spec,
-            originator = SciMLBase.ChainRulesOriginator(),
+            originator = SciMLBase.set_mooncakeoriginator_if_mooncake(SciMLBase.ChainRulesOriginator()),
             verbose,
             kwargs...))
     else
@@ -100,7 +100,7 @@ function solve(prob::AbstractNonlinearProblem, args...; sensealg = nothing,
             p,
             args...;
             alias = alias_spec,
-            originator = SciMLBase.ChainRulesOriginator(),
+            originator = SciMLBase.set_mooncakeoriginator_if_mooncake(SciMLBase.ChainRulesOriginator()),
             verbose,
             kwargs...)
     end

lib/NonlinearSolveBase/src/utils.jl

@@ -320,6 +320,4 @@ function clean_sprint_struct(x, indent::Int)
     return "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))"
 end
 
-set_mooncakeoriginator_if_mooncake(x::SciMLBase.ADOriginator) = x
-
 end