Use nutpie by default

[Jayant-kernel]

Closes 8079

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[Jayant-kernel]

@ricardoV94
I've opened a draft PR for this here:

It implements the auto-selection logic:
if nutpie is installed and the model is suitable (all continuous variables), it will be used by default when nuts_sampler=None. It falls back to pymc
otherwise.

Let me know what you think!

[ricardoV94]

nutpie will be a default dependency once we do these changes, no need to check if it's installed

[ricardoV94]

compile kwargs is not enough to rule out nutpie. Only if it implies a pytensor compilation mode that is not numba or jax backend. Something like nutpie_compatibile_mode = isinstance(get_mode(compile_kwargs.get("mode")).linker, JAXLinker| NumbaLinker)

[ricardoV94]

We also need to propagate this information into the backend kwarg for nutpie

[ricardoV94]

no reason for a new test file, it should be in test_mcmc, or whatever file tests sample functionality now

[Jayant-kernel]

@ricardoV94 T
hanks again for the patience and the detailed review! I've now addressed all the feedback and fixed the CI issues:

1. Removed _nutpie_is_installed() — nutpie is now treated as a default dependency.
2. Proper Linker Detection — Implemented the check using isinstance(get_mode(...).linker, JAXLinker | NumbaLinker) (using union syntax to satisfy Ruff UP038).
3. Backend Propagation — Added logic to set backend="jax" or backend="numba" for nutpie based on the PyTensor linker.
4. Moved Tests — Deleted test_nutpie_selection.py and moved all tests into tests/sampling/test_mcmc.py.
5. Fixed Pre-commit — Fixed all trailing whitespace, import sorting, and Ruff formatting issues (v0.11.13).

All CI checks (Docs, Pre-commit, etc.) are now passing (green). Ready for re-review!

[twiecki]

@ricardoV94 wdyt, would be nice to get this default on the v6 branch.

[ricardoV94]

Closing in favor of #8248