docs: fix initialization tutorial example to use D(x) instead of y

The documentation example for a well-conditioned initialization system was
using `[x => 1, y => 0.0, g => 1]` which results in a structurally singular
system (returning NonlinearLeastSquaresProblem).

Changed to `[x => 1, D(x) => 0.0, g => 1]` with `guesses = [λ => 1, y => 0]`
which properly specifies the derivative and results in a well-conditioned
NonlinearProblem (actually SCCNonlinearProblem) as intended.

Also fixed "NonlinearSystem" -> "NonlinearProblem" which is the correct type.

Fixes #4024

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

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

Author: ChrisRackauckas

docs/src/tutorials/initialization.md

@@ -477,10 +477,10 @@ In comparison, if we have a well-conditioned system:
 
 ```@example init
 iprob = ModelingToolkit.InitializationProblem(pend, 0.0,
-    [x => 1, y => 0.0, g => 1], guesses = [λ => 1])
+    [x => 1, D(x) => 0.0, g => 1], guesses = [λ => 1, y => 0])
 ```
 
-notice that we instead obtained a NonlinearSystem. In this case we have to use
+notice that we instead obtained a NonlinearProblem. In this case we can use
 different solvers which can take advantage of the fact that the Jacobian is square.
 
 ```@example init