REF: Migrate to ArviZ 1.0 (InferenceData -> DataTree)

[AAlexxis222]

Migrates pymc-extras to support ArviZ 1.0, replacing InferenceData with xarray.DataTree.

Changes:

• Imports: Replaced arviz.InferenceData with xarray.DataTree.
• Attributes: Refactored .posterior access to dictionary style (["posterior"]).
• API: Updated constructors (DataTree.from_dict) and replaced .extend() with .update().

Verification:

• ~325 tests passing (verified against PyMC PR #8019 rebase).
• Validated prior and pathfinder modules.

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[aloctavodia]

In many places you are apllying formating issues. Are you sure these are needed?

[AAlexxis222]

Hi! Yes, I applied the formatting tools (black, isort, ruff) because the pre-commit CI job was failing with linting errors on the modified files.

I wanted to ensure the CI was green. However, if you prefer to keep the diff minimal, I can try to revert the style changes and only keep the logic migration (though pre-commit might fail again)

[aloctavodia]

That's fine, just checking.