Turing performance, debugging and benchmarks meta issue

[shravanngoswamii]

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

• Better performance guidelines and support for user #702 (better performance guidelines: benchmark and profile a model, choose an AD backend, write efficient models)
• Question about custom inference parameterized by distribution types Turing.jl#564 (a page on debugging tools)
• Depend on Bijectors Turing.jl#565 (tips on optimising performance)
• LDA Model incredibly slow, even in low dimension 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, Depend on Bijectors Turing.jl#565)
• A page on model debugging tools: check_model, model_warntype, and related utilities (Add a page on debugging tools for Turing models #564)
• Remove references to the archived ADTests site
• A guide on interpreting chain summary statistics (ess, rhat, mcse) and diagnosing MCMC problems (More guides on how to interpret chain results and debugging MCMC #668)

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