Deprecate AdvancedVI or move it outside TuringLang

Variational inference methods are often difficult to scale to complex models with strong or structured parameter dependencies. Their performance can depend heavily on the variational family, parameterisation, gradient estimator, and optimisation method, while more expressive approximations add substantial implementation complexity. This makes VI an area where researchers should be able to experiment with new methods without requiring those methods to become part of Turing.jl or DynamicPPL.

AdvancedVI therefore does not need to live inside either Turing.jl or DynamicPPL. It can instead be maintained as an independent inference package operating against a generic log-density and gradient interface. Turing models can expose the required log density and derivatives through that interface, allowing AdvancedVI, or other VI implementations, to be applied to Turing models without depending on Turing's internal model representation.

This separation would give VI implementations more freedom to evolve independently while keeping Turing.jl and DynamicPPL focused on modelling and model execution. It would also make the boundary clearer: Turing provides models and exposes their log densities and gradients; AdvancedVI provides variational inference algorithms that consume that interface.

No files, tests, or entry points are named. Start by reviewing AdvancedVI's public interfaces and its interaction with Turing.jl and DynamicPPL, then determine whether the package should be deprecated or moved behind a generic log-density and gradient interface. Done requires an agreed package boundary and an implementation plan.