Add __init and __solve dispatches for AbstractSteadyStateProblem

This PR adds default algorithm dispatches for AbstractSteadyStateProblem
to use the same defaults as NonlinearProblem. The implementation mirrors
the existing NonlinearProblem dispatches to ensure consistent behavior.

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

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

Author: ChrisRackauckas

src/default.jl

@@ -37,6 +37,34 @@ function SciMLBase.__solve(prob::NonlinearProblem, ::Nothing, args...; kwargs...
     )
 end
 
+function SciMLBase.__init(prob::SciMLBase.AbstractSteadyStateProblem, ::Nothing, args...; kwargs...)
+    must_use_jacobian = Val(SciMLBase.has_jac(prob.f))
+    return SciMLBase.__init(
+        prob,
+        FastShortcutNonlinearPolyalg(
+            eltype(prob.u0); must_use_jacobian, u0_len = length(prob.u0)
+        ),
+        args...;
+        kwargs...
+    )
+end
+
+function SciMLBase.__solve(prob::SciMLBase.AbstractSteadyStateProblem, ::Nothing, args...; kwargs...)
+    must_use_jacobian = Val(SciMLBase.has_jac(prob.f))
+    prefer_simplenonlinearsolve = Val(prob.u0 isa StaticArray)
+    return SciMLBase.__solve(
+        prob,
+        FastShortcutNonlinearPolyalg(
+            eltype(prob.u0);
+            must_use_jacobian,
+            prefer_simplenonlinearsolve,
+            u0_len = length(prob.u0)
+        ),
+        args...;
+        kwargs...
+    )
+end
+
 function SciMLBase.__init(prob::NonlinearLeastSquaresProblem, ::Nothing, args...; kwargs...)
     return SciMLBase.__init(
         prob, FastShortcutNLLSPolyalg(eltype(prob.u0)), args...; kwargs...