Changing transposing instruments with multiple staves changes notes if the instrument change is made in the lower staff

Issue type

UX/Interaction bug (incorrect behaviour)

Description with steps to reproduce

1. Open a score with a transposing instrument, for example a Clarinet in Bb.
2. Add another staff to the clarinet.
3. Write a melody in the lower staff and paste it in the upper one, so that both staves have the same.
4. Change to another instrument in the middle of the melody in the LOWER staff, for example to a Horn in F, and see that both staves are the same.
5. Save the score.
6. Close the score.
7. Open the score again.
8. See that the upper staff is a mess after the instrument change.

Expected behaviour: When opening the score again, it should be the same as before closing it.
Current behaviour: The upper staff changes notes and playback after the instrument change. It is like Musescore doesn't recognise the key change.

ATTENTION: The bug only appears when a transposing instrument is involved, and when they are in different keys, so here is a small summary: (TI: Transposing instrument; NTI: Non transposing instrument).

TI -> TI (different key): Bug appears.
TI -> TI (same key): No bug.
TI -> NTI: Bug appears.
NTI -> TI: Bug appears.
NTI -> NTI: No bug.

It also happens between the same transposing instrument, for example, from Clarinet in Bb to Clarinet in A.

It is necessary that the instrument change is made in the LOWER staff, because when it is made in the upper staff there is no bug.

Supporting files, videos and screenshots

What appears before closing the score and what should appear when opening it again.

What actually appears when opening it.

What is the latest version of MuseScore Studio where this issue is present?

OS: Windows 11 Version 2009 or later, Arch.: x86_64, MuseScore Studio version (64-bit): 4.4.1-242490810, revision: github-musescore-musescore-0b3dd00

Regression

I was unable to check

Operating system

Windows 11

Additional context

No response

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 with a multi-staff transposing instrument, changing instruments in the lower staff, then saving, closing, and reopening the score. Trace the save and reload handling for instrument changes and multi-staff transposition; done means the upper staff retains its notes and playback after reopening.