### 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
accept->set_text(TTR("Couldn't save new scene. Likely dependencies (instances) couldn't be satisfied."));
			accept->popup_centered();
			return;
		}
		int flg = 0;
		if (EDITOR_GET("filesystem/on_save/compress_binary_resources")) {
			flg |= ResourceSaver::FLAG_COMPRESS;
		}
		err = ResourceSaver::save(sdata, p_file, flg);
		if (err != OK) {
			accept->set_text(TTR("Error saving scene."));
			accept->popup_centered();
			return;
		}
		_replace_with_branch_scene(p_file, base);
	} else {
		accept->set_text(TTR("Error duplicating scene to save it."));
		accept->popup_centered();
		return;
	}
}
void SceneTreeDock::_set_node_owner_recursive(Node *p_node, Node *p_owner) {
	if (!p_node->get_owner()) {
		p_node->set_owner(p_owner);
	}
	for (int i = 0; i < p_node->get_child_count(false); i++) {
		_set_node_owner_recursive(p_node->get_child(i, false), p_owner);
	}
}
static bool _is_node_visible(Node *p_node) {