Part names are not synced with instrument names / mixer

Issue type

Other type of issue

Bug description

If you edit the name of an instrument then the part name is not updated to match, and vice versa.

The problem is particularly bad when changing instrument numbers (e.g. renaming "Flute 2" to "Flute 1"). After renaming the instrument, the part will still be called "Flute 2", which is confusing.

Also, if you subsequently add another flute instrument then the newly generated part will also be called "Flute 2", so now you have two parts both called "Flute 2".

This file had some instruments that I deleted and created new ones. The new instrument are numbered in addition to the old (deleted ones), I then changed the name of the instruments to what I need but in exportation MU does not update the changed names.

Steps to reproduce

1. create new file with two instruments (Flute for ex.)
2. add another instrument of the same type (you should see now flute 1, 2 ,3)
3. delete flute 1
4. rename flutes 2, and 3 as 1 and 2
5. open the Parts dialog or the Export dialog
6. you should see flute 2 (instead of one) and flute with no number. Although in the file they are correctly named flute 1 and 2.

MuseScore Version

4.0.2

Regression

I don't know

Operating system

MacOs 13.2.1

Additional context

Instrument names are displayed inside the:

• score
• Instruments panel
• Staff/part properties dialog.

Part names are displayed inside the:

• Parts dialog
• Export dialog.