Part name changes after accessing Staff/part-properties dialog reset to default

Issue type

UX/Interaction bug (incorrect behaviour)

Bug description

When you access the Staff/part-properties dialog and click OK (with or without making a change), the name of the part is changed.

I.e. you first setup the score and generate parts. You then rename the parts to give them an appropiate name.
Later you decide you need to make a change to the staff/properties, after doing this the name of the part is suddenly changed to the original instrument name.
After this, when you repeat this for a second staff, the part name changes to the instrument name + (1).

Logic discovered by Steven_e007 see: https://musescore.org/en/node/360213

Steps to reproduce

1. Create a new score
2. Add an instrument
3. Click Done
4. Now add a second instance of the same instrument
5. Change the name of the FIRST instrument and add 1 (as now you have a Instrument 1 and Instrument 2).
6. Click the Part button and rename the parts here as well
7. Click open all, to ensure the parts are generated.
8. Go back to the main score and right-click the top instrument staff and select Staff/part-properties
9. Make a change OR just click OK to close the dialog
10. Observe the name of the part has now changed (check the TAB)
11. Now right-click the second instrument staff and select Staff/part-properties
12. Make a change OR just click OK to close the dialog
13. Observe the name of the part has now changed (check the TAB)
14. Open the Part dialog, the part name rename can be seen here as well

See also the attached video.

Screenshots/Screen recordings

Easy steps to reproduce:

1. Open part
2. Rename part (in Parts dialog)
3. In Score, select that staff and open Staff/Part properties
4. Click OK

https://github.com/musescore/MuseScore/assets/90187801/26c9bf81-8fd4-4dcd-933c-9d79c6d1a8ad

MuseScore Version

4.2.1

Regression

No.

Operating system

Windows 11

Additional context

No response