Make ProblemTypeCtx public API (#4842)

`ProblemTypeCtx` is the documented metadata key that controls
`prob.problem_type`, read by `ODEProblem` and `NonlinearProblem`
construction. SciMLBase's `wrap_sol` dispatches on that value, so PDE
discretization packages must set it to have their solutions wrapped in
`PDETimeSeriesSolution` / `PDENoTimeSolution`. It is a cross-package
protocol key, but was neither exported nor `public`, so downstream users
had no non-internal way to reach it.

Mark it `@public` and add it to the rendered docs. `MTKVariableTypeCtx`
is already public, so this follows the existing treatment of metadata
context types.



Claude-Session: https://claude.ai/code/session_0117aJvytDT3y2jMi5Ng6Q5m

Co-authored-by: ChrisRackauckas-Claude <accounts@chrisrackauckas.com>
Co-authored-by: Claude Opus 5 (1M context) <noreply@anthropic.com>

Author: 3 people

docs/src/API/problems.md

@@ -48,6 +48,16 @@ SciMLBase.HomotopyNonlinearFunction
 SciMLBase.LinearProblem
 ```
 
+## Problem type metadata
+
+Systems can carry a `problem_type` that is forwarded to the constructed problem. This is
+how discretization packages attach their own metadata to a generated problem and recover
+it downstream, for example to wrap a solution in a richer solution type.
+
+```@docs
+ModelingToolkit.ProblemTypeCtx
+```
+
 ## Optimization and optimal control
 
 ```@docs

lib/ModelingToolkitBase/Project.toml

@@ -1,7 +1,7 @@
 name = "ModelingToolkitBase"
 uuid = "7771a370-6774-4173-bd38-47e70ca0b839"
 authors = ["Yingbo Ma <mayingbo5@gmail.com>", "Chris Rackauckas <accounts@chrisrackauckas.com> and contributors"]
-version = "1.57.1"
+version = "1.58.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

lib/ModelingToolkitBase/src/ModelingToolkitBase.jl

@@ -406,6 +406,7 @@ const set_scalar_metadata = setmetadata
 @public Both
 @public SymbolicADDisallowed, check_symbolic_ad_allowed
 @public tobrownian, toparam
+@public ProblemTypeCtx
 
 for prop in [SYS_PROPS; [:continuous_events, :discrete_events]]
     getter = Symbol(:get_, prop)