[A2ELAOUDI]

Description

When apply_ufunc fails on a Dataset, the error comes from code that only sees a Variable, so it can't say which data variable broke. As discussed in #2078, threading the name through broadcast_compat_data and apply_variable_ufunc would add a lot of plumbing for an error message. Instead, apply_dict_of_variables_vfunc adds a note to the exception, the same pattern already used in conventions.py and backends/common.py:

ValueError: operand to apply_ufunc encountered unexpected dimensions ['y'] on an input variable: these are core dimensions on other input or output variables
Raised while applying function to variable 'status'

The exception type and message are unchanged, so existing except/match= code keeps working. Errors raised by the user's function get the same note.

Checklist

• Closes apply_ufunc should include variable names in error messages #2078
• Tests added
• User visible changes (including notable bug fixes) are documented in whats-new.rst

AI Disclosure

• This PR contains AI-generated content.
  • I have tested any AI-generated content in my PR.
  • I take responsibility for any AI-generated content in my PR.
    Tools: Claude Code (Claude Opus 5.5)

[This is Claude Code on behalf of Abderrahmane El Aoudi]

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