Clean up LogDensityFunctions interface code + `setADtype`

[penelopeysm]

Turing.jl/src/mcmc/Inference.jl

Lines 193 to 211 in 24d5556

	function LogDensityProblemsAD.ADgradient(ℓ::DynamicPPL.LogDensityFunction)
	return LogDensityProblemsAD.ADgradient(getADType(DynamicPPL.getcontext(ℓ)), ℓ)
	end
	function LogDensityProblems.logdensity(
	f::Turing.LogDensityFunction{<:AbstractVarInfo,<:Model,<:DynamicPPL.DefaultContext},
	x::NamedTuple,
	)
	return DynamicPPL.logjoint(f.model, DynamicPPL.unflatten(f.varinfo, x))
	end
	# TODO: make a nicer `set_namedtuple!` and move these functions to DynamicPPL.
	function DynamicPPL.unflatten(vi::TypedVarInfo, θ::NamedTuple)
	set_namedtuple!(deepcopy(vi), θ)
	return vi
	end
	function DynamicPPL.unflatten(vi::SimpleVarInfo, θ::NamedTuple)
	return SimpleVarInfo(θ, vi.logp, vi.transformation)
	end

This code looks suspiciously similar to existing code in DynamicPPL, and in any case is type piracy and should be moved there or deleted as appropriate.

Unsure why Aqua doesn't flag this.

[penelopeysm]

Oh, I see, the ADgradient method is a single-argument version that automatically 'detects' the AD backend, as opposed to the usual two-argument method which takes the AD backend as the first argument.

Still type piracy though, should be given its own name imo.

[penelopeysm]

This code should be removable after TuringLang/DynamicPPL.jl#806 is merged

[penelopeysm]

Closed by #2490, also in 0.37.0 now