Interop: native PowerDiff.jl backend (100% fidelity bridge) #48

Goal

Add a native PowerIO ingest backend to PowerDiff.jl so a case parsed by PowerIO can populate PowerDiff's network and problem types without a second source parse.

PowerDiff owns differentiable formulations, KKT systems, solves, and sensitivity policy. PowerIO owns source models, indexed problem input data, and optional generic matrix projections.

Scope

• Map PowerIO's balanced Network and model JSON onto PowerDiff's AC/DC network types and id mapping.
• Evaluate powerio-prob::DcOpfInstance as the indexed DC input boundary. Keep PowerDiff's variable stacks and solver formulation in PowerDiff.
• Audit base_mva, units, branch parameters, costs, loads, shunts, status flags, reference buses, source IDs, and dense indices.
• Compare derived operators against PowerDiff's native builders on case9, case14, case30, and PEGASE cases.
• Add a PowerDiff backend over PowerIO.jl or the C ABI.
• Add a cross validation harness that compares the PowerIO backed model with PowerDiff's native parser.

Current dependencies

The C Arrow table transport from #38 and the PowerIO.jl scaffold have landed. #238 defines the problem instance boundary. #246 keeps solver formulations and KKT assembly out of powerio-prob.

Lock the target mapping against a stable PowerDiff backend API before implementation.