`Save selection` does not work for parts

Issue type

Opening/saving issue

Description with steps to reproduce

Save selection does not save selections in parts. Instead, it exports any current selection in the main score, or fails if there is no selection in the main score.

1. Create or open an existing score.
2. Ensuring that nothing is selected in the score, open a part with some musical content.
3. File > Save selection
4. Confirm the save location
   RESULT: Error: Your score could not be saved. The selection is empty.

Repeat the steps above, but with a selection in the score before switching to the part in step 2.
RESULT: The selection in the score is saved, rather than any selection in the part.

Supporting files, videos and screenshots

https://github.com/user-attachments/assets/518ad0d5-3954-4fc4-987d-46f5bfe19a67

In which versions of MuseScore Studio is this issue present?

4.0.0 - latest nightlies

Regression

Yes, this used to work in MuseScore 3.x and now is broken

Operating system

Ubuntu 24.04.4 LTS, Windows 11

Additional context

This appears to have been working in 3.6.2. It silently fails in 4.0.x, and since 4.1.x the error message is shown.

Checklist

• This report follows the guidelines for reporting bugs and issues
• I have verified that this issue has not been logged before, by searching the issue tracker for similar issues
• I have attached all requested files and information to this report
• I have attempted to identify the root problem as concisely as possible, and have used minimal reproducible examples where possible

Reproduce the issue by opening a part with musical content and using File > Save selection, first with and then without a selection in the main score. Trace the save-selection handling to determine why it uses the main score instead of the current part. Done means a selection in a part is saved, and an empty part selection no longer incorrectly depends on the main score.