fix: don't leak aux coords of summed dims onto the term dimension

[FBumann]

Fixes the remaining alignment-leak half of #295.

Note

The following content was generated by AI.

Changes proposed in this Pull Request

LinearExpression._sum drops a summed dimension's index coordinates via reset_index, but an auxiliary (non-dimension) coordinate on that dimension — e.g. a B(A) group label — rode the .stack() onto the internal _term helper dimension. The leaked coordinate then broke later arithmetic:

>>> v = v.assign_coords({"B": ("A", [311, 311, 322])})
>>> (1 * v).sum("A") >= xr.DataArray(10)
CoordinateValidationError: coordinate B has dimensions ('_term',), but these are not a subset of the DataArray dimensions ()

Aux coords whose dims intersect the summed dims are now dropped before stacking. Aux coords on the remaining dimensions still propagate unchanged. QuadraticExpression.sum and the groupby fallback route through the same _sum and are covered by the same change.

Only the leak is fixed here — it is a plain bug under both semantics. The other half of #295's residual (a conflicting aux coord being silently kept in binary operations) is a semantics change and stays with the v1 work (convention §11).

Checklist

• AI-generated content is marked (see AGENTS.md).
• Code changes are sufficiently documented.
• Unit tests for new features were added: aux coord on a summed dim is dropped (incl. the Auxiliary non-dimension coordinates leak into expressions and break alignment #295 reproducer), aux coord on a kept dim propagates.
• A note for the release notes doc/release_notes.rst of the upcoming release is included.
• I consent to the release of this PR's code under the MIT license.

[codspeed-hq]

Merging this PR will not alter performance

✅ 173 untouched benchmarks
⏩ 173 skipped benchmarks¹

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_{Comparing fix-295-aux-coord-term-leak (7fb776a) with master (c02f5db)}

Footnotes

1. 173 benchmarks were skipped, so the baseline results were used instead. If they were deleted from the codebase, click here and archive them to remove them from the performance reports. ↩