Add unified Traits module for control-toolbox ecosystem

[ocots]

Context

The control-toolbox ecosystem currently has trait definitions scattered across packages:

• CTFlows: Has a Traits submodule with mutability, AD, variable costate, time dependence, etc.
• CTModels: Has trait-like types (TimeDependence, ObjectiveForm, TimeBoundaryType, TimeGridType) that should be traits

These traits describe structural properties of optimal control problems and flows, and should be shared across the ecosystem at the base layer.

Task

Create a unified Traits module in CTBase that will contain all trait definitions for the control-toolbox ecosystem.

Traits to include

From CTFlows (existing):

• AbstractTrait, AbstractModeTrait, AbstractContentTrait
• AbstractMutabilityTrait, InPlace, OutOfPlace
• AbstractADTrait, WithAD, WithoutAD
• AbstractVariableCostateCapability, SupportsVariableCostate, NoVariableCostate
• PointTrait, TrajectoryTrait
• StateTrait, HamiltonianTrait, AugmentedHamiltonianTrait
• VariableDependence, Fixed, NonFixed
• Time dependence traits (currently re-exported from CTModels)
• Query functions: is_inplace, is_outofplace, ad_trait, variable_costate_trait, etc.

From CTModels (to migrate):

• TimeDependence, Autonomous, NonAutonomous
• ObjectiveForm, MayerForm, LagrangeForm, BolzaForm
• TimeBoundary, FixedTime, FreeTime
• TimeGridStrategy, UnifiedGrid, MultipleGrid

Module structure

src/Traits/
├── Traits.jl              # Module manifest
├── abstract.jl            # Base trait abstractions
├── mutability.jl          # InPlace/OutOfPlace
├── ad.jl                  # WithAD/WithoutAD
├── variable_costate.jl    # Variable costate capability
├── mode.jl                # Point/Trajectory
├── content.jl            # State/Hamiltonian/AugmentedHamiltonian
├── time_dependence.jl    # Autonomous/NonAutonomous
├── objective_form.jl      # Mayer/Lagrange/Bolza
├── time_boundary.jl       # FixedTime/FreeTime
├── time_grid.jl           # UnifiedGrid/MultipleGrid
├── variable_dependence.jl # Fixed/NonFixed
└── helpers.jl             # Query functions

Required actions

1. Create src/Traits/ directory with the structure above
2. Implement all trait types and query functions
3. Add comprehensive docstrings
4. Export all public traits and query functions
5. Ensure no dependencies on CTModels or CTFlows (CTBase is the base layer)

Related issues

• CTFlows: Move Traits module to CTBase CTFlows.jl#246 — Move traits from CTFlows to CTBase
• CTModels: https://github.com/control-toolbox/CTModels.jl/issues/XXX — Move traits from CTModels to CTBase

Priority

High — This is a foundational refactoring that will improve code organization and enable better type-based dispatch across the ecosystem.