If anyone is interested.
You can overwrite the methods used by your CustomPaletteProvider directly in your CustomPalette(Provider) like this:
constructor(create, elementFactory, palette, translate) {
this.create = create;
this.elementFactory = elementFactory;
this.translate = translate;
palette.registerProvider(this);
// https://github.com/bpmn-io/diagram-js/blob/master/lib/features/palette/Palette.js#L186
palette._update = function () {
// Replace functionality. In my case
// * I copied the function from the link above,
// * replaced `this.` by `palette.`
// * and imported all missing packages
...
// * to set the id, i added the following lines
if (entry.id) {
domAttr(control, 'id', entry.id)
}
...
}
}