Turing performance, debugging and benchmarks meta issue

Tracking issue for documentation on measuring and improving the performance of Turing models, and on debugging them. It collects the following:

• TuringLang/docs#702 (better performance guidelines: benchmark and profile a model, choose an AD backend, write efficient models)
• TuringLang/Turing.jl#564 (a page on debugging tools)
• TuringLang/Turing.jl#565 (tips on optimising performance)
• TuringLang/Turing.jl#668 (interpreting chain summary statistics and debugging MCMC)

What the docs cover today

• Choosing an AD backend: Automatic Differentiation (heuristics, run_ad benchmarking) and a FAQ entry.
• Writing efficient models: Performance Tips (multivariate distributions, AD backend choice, type stability).
• Error-level debugging: Troubleshooting.

Note that TuringBenchmarking.jl is deprecated. The current tool is DynamicPPL.TestUtils.AD.run_ad, which gives primal and gradient timings per backend.

Remaining work

• Benchmarking and profiling guidance (Turing.jl#2414, TuringLang/Turing.jl#565)
• A page on model debugging tools: check_model, model_warntype, and related utilities (#564)
• Remove references to the archived ADTests site
• A guide on interpreting chain summary statistics (ess, rhat, mcse) and diagnosing MCMC problems (#668)

The first three items are addressed by the linked PR. The last is a larger writing task and is left open here.

Start with Turing.jl#668 and review the existing Automatic Differentiation, Performance Tips, and Troubleshooting pages linked in this issue. Define the guide’s scope around interpreting ess, rhat, and mcse and diagnosing MCMC problems. Done means the remaining documentation task is covered with a clear, usable guide.