### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
}
	help_menu->set_item_icon(help_menu->get_item_index(HELP_SEARCH), theme->get_icon(SNAME("HelpSearch"), EditorStringName(EditorIcons)));
	help_menu->set_item_icon(help_menu->get_item_index(HELP_DOCS), theme->get_icon(SNAME("ExternalLink"), EditorStringName(EditorIcons)));
	help_menu->set_item_icon(help_menu->get_item_index(HELP_QA), theme->get_icon(SNAME("ExternalLink"), EditorStringName(EditorIcons)));
	help_menu->set_item_icon(help_menu->get_item_index(HELP_REPORT_A_BUG), theme->get_icon(SNAME("ExternalLink"), EditorStringName(EditorIcons)));
	help_menu->set_item_icon(help_menu->get_item_index(HELP_COPY_SYSTEM_INFO), theme->get_icon(SNAME("ActionCopy"), EditorStringName(EditorIcons)));
	help_menu->set_item_icon(help_menu->get_item_index(HELP_SUGGEST_A_FEATURE), theme->get_icon(SNAME("ExternalLink"), EditorStringName(EditorIcons)));
	help_menu->set_item_icon(help_menu->get_item_index(HELP_SEND_DOCS_FEEDBACK), theme->get_icon(SNAME("ExternalLink"), EditorStringName(EditorIcons)));
	help_menu->set_item_icon(help_menu->get_item_index(HELP_COMMUNITY), theme->get_icon(SNAME("ExternalLink"), EditorStringName(EditorIcons)));
	help_menu->set_item_icon(help_menu->get_item_index(HELP_ABOUT), theme->get_icon(SNAME("Godot"), EditorStringName(EditorIcons)));
	help_menu->set_item_icon(help_menu->get_item_index(HELP_SUPPORT_GODOT_DEVELOPMENT), theme->get_icon(SNAME("Heart"), EditorStringName(EditorIcons)));
	for (int i = 0; i < main_editor_buttons.size(); i++) {
		main_editor_buttons.write[i]->add_theme_font_override("font", theme->get_font(SNAME("main_button_font"), EditorStringName(EditorFonts)));
		main_editor_buttons.write[i]->add_theme_font_size_override("font_size", theme->get_font_size(SNAME("main_button_font_size"), EditorStringName(EditorFonts)));
	}
	if (EditorDebuggerNode::get_singleton()->is_visible()) {
		bottom_panel->add_theme_style_override("panel", theme->get_stylebox(SNAME("BottomPanelDebuggerOverride"), EditorStringName(EditorStyles)));
	}
	for (int i = 0; i < main_editor_buttons.size(); i++) {
		Button *tb = main_editor_buttons[i];
		EditorPlugin *p_editor = editor_table[i];
		Ref<Texture2D> icon = p_editor->get_icon();
		if (icon.is_valid()) {
			tb->set_icon(icon);
		} else if (theme->has_icon(p_editor->get_name(), EditorStringName(EditorIcons))) {
			tb->set_icon(theme->get_icon(p_editor->get_name(), EditorStringName(EditorIcons)));
		}
	}
}
void EditorNode::update_preview_themes(int p_mode) {