### Godot version

v4.1.1.stable.official [bd6af8e0e]

### System information

Godot v4.1.1.stable - Debian GNU/Linux trixie/sid trixie - Vulkan (Compatibility) - Mesa Intel(R) HD Graphics 520 (SKL GT2) () - Intel(R) Core(TM) i7-6500U CPU @ 2.50GHz (4 Threads)

### Issue description

After right clicking in thet "Filter Nodes" menu in the scene tree dock, the sub-menu is populated with a "Search" icon.

If I later switch themes in the same session, this icon is never updated to match the new theme.

![image](https://github.com/godotengine/godot/assets/660911/14336bb3-12ca-48c8-b030-8ada6ac27ec6)


### Steps to reproduce

1. Right click in the "Filter Nodes" menu in scene tree dock
2. Switch themes
3. Right click again in the "Filter Nodes" menu

Expected result: Icon has updated to match the theme I am currently using
Actual result: Icon is still using the theme I launched Godot with

### Minimal reproduction project

N/A
if (profile_allow_editing) {
		bool add_separator = false;
		if (full_selection.size() == 1) {
			add_separator = true;
			menu->add_icon_shortcut(get_theme_icon(SNAME("Rename"), SNAME("EditorIcons")), ED_GET_SHORTCUT("scene_tree/rename"), TOOL_RENAME);
		}
		bool can_replace = true;
		for (Node *E : selection) {
			if (E != edited_scene && (E->get_owner() != edited_scene || !E->get_scene_file_path().is_empty())) {
				can_replace = false;
				break;
			}
		}
		if (can_replace) {
			add_separator = true;
			menu->add_icon_shortcut(get_theme_icon(SNAME("Reload"), SNAME("EditorIcons")), ED_GET_SHORTCUT("scene_tree/change_node_type"), TOOL_REPLACE);
		}
		if (scene_tree->get_selected() != edited_scene) {
			if (add_separator) {
				menu->add_separator();
			}
			menu->add_icon_shortcut(get_theme_icon(SNAME("MoveUp"), SNAME("EditorIcons")), ED_GET_SHORTCUT("scene_tree/move_up"), TOOL_MOVE_UP);
			menu->add_icon_shortcut(get_theme_icon(SNAME("MoveDown"), SNAME("EditorIcons")), ED_GET_SHORTCUT("scene_tree/move_down"), TOOL_MOVE_DOWN);
			menu->add_icon_shortcut(get_theme_icon(SNAME("Duplicate"), SNAME("EditorIcons")), ED_GET_SHORTCUT("scene_tree/duplicate"), TOOL_DUPLICATE);
			menu->add_icon_shortcut(get_theme_icon(SNAME("Reparent"), SNAME("EditorIcons")), ED_GET_SHORTCUT("scene_tree/reparent"), TOOL_REPARENT);
			menu->add_icon_shortcut(get_theme_icon(SNAME("ReparentToNewNode"), SNAME("EditorIcons")), ED_GET_SHORTCUT("scene_tree/reparent_to_new_node"), TOOL_REPARENT_TO_NEW_NODE);
			if (selection.size() == 1) {
				menu->add_icon_shortcut(get_theme_icon(SNAME("NewRoot"), SNAME("EditorIcons")), ED_GET_SHORTCUT("scene_tree/make_root"), TOOL_MAKE_ROOT);
			}
		}