Palette selection is not honoured in new scores until MuseScore is closed and restarted

Describe the bug
If you change the palettes shown in the side bar by adding or hiding a palette and then (without closing MuseScore) create a new score or open an existing score, the new instance of MuseScore reverts to the "old" palette selection.

To Reproduce

Steps to reproduce the behavior:

1. Ensure there are no running instances of Musescore
2. Start MuseScore
3. Create a new score
4. Save the score - call it "OLD"
5. Add a palette to the side bar by clicking on the "+" and selecting a palette
6. Create a new score
7. Note that the palette added in step 5 is not shown.
8. Close all instances of MuseScore
9. Restart Musescore
10. Create a new Score
11. Note that palette added in step 5 is shown
12. Open "OLD" score created in step 4
13. Note that palette added in step 5 (after "OLD" was saved) is shown.

Expected behavior

Palette setup should be preserved when a new score (and new instance of Musescore) is created.

Palette setup should be saved with the score and used when the score is re-opened.

Screenshots
If applicable, add screenshots to help explain your problem.

Platform information
OS: Windows 10 Version 2009, Arch.: x86_64, MuseScore version (64-bit): 4.0.0-3278824640, revision: github-musescore-musescore-abc123456

Additional context

Having created a useful set up, a user wishing to create a new score and take advantage of the new setup will be disappointed unless Musescore is closed and re-opened as otherwise that carefully crafted set up will not be used for the new score.

Start by reproducing the palette-sidebar workflow described: change the palette selection, create a new score, and reopen the saved OLD score without restarting MuseScore. Trace how palette setup is carried between score instances and saved scores; done means the changed palette selection is used for new scores and preserved when scores are reopened.