Palettes and palette items not allowed to be re-arranged during palette search

Issue type

UI bug

Bug description

In MuseScore 3, one can re-arrange the palette search results to be in accord with what comes with priority, either as a palette or as a palette item. For example:

1. I type bass and get clefs but want rather the 8va to show up first. What i can do is re-arrange it and next time around it will be first on the results.

https://github.com/musescore/MuseScore/assets/7139517/88963f77-396a-48a0-b3e9-6cc061404198

2. Similarly, I can also re-arrange palette items in 3.6 for the same purpose (for example rearranging the p dynamics):

https://github.com/musescore/MuseScore/assets/7139517/d2682245-2196-415c-8ca2-4b49de8b8e9b

Steps to reproduce

Now let's look at MuseScore 4.1:

https://github.com/musescore/MuseScore/assets/7139517/c4ae7a37-3954-4662-8b24-1b6743124541

None of the demonstrated functionality of MS3 works here.

P.S. It looks like during palette search there is no honoring of any customization generally speaking. If the user re-arranges something while not in palette-search, the results will still read from the "default" palette arrangements or something.

MuseScore Version

4.1

Regression

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

Operating system

LNX XFCE

Additional context

Again, this along with no custom palettes showing up in search and the lack of bringing the tab to the forefront for triggering it, now that I realize it... has led to my forgetting about MS4.1/2 for now and will come back later hoping in the next year or so to have the same functionality as I've had for the past 4 years with MS3 :) I'd try to help with the code, but it's too tightly packed and seemingly "indirect" for my current programming skills coming in for the first time to be efficient with time and functionality. Good luck to those responsible!