### 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
#include "scene/property_utils.h"
#include "scene/resources/packed_scene.h"
#include "servers/display_server.h"
#include "servers/rendering_server.h"
#include "modules/modules_enabled.gen.h" 
#ifdef MODULE_REGEX_ENABLED
#include "editor/rename_dialog.h"
#endif 
void SceneTreeDock::_nodes_drag_begin() {
	pending_click_select = nullptr;
}
void SceneTreeDock::_quick_open() {
	instantiate_scenes(quick_open->get_selected_files(), scene_tree->get_selected());
}
void SceneTreeDock::input(const Ref<InputEvent> &p_event) {
	ERR_FAIL_COND(p_event.is_null());
	Ref<InputEventMouseButton> mb = p_event;
	if (mb.is_valid() && (mb->get_button_index() == MouseButton::LEFT || mb->get_button_index() == MouseButton::RIGHT)) {
		if (mb->is_pressed() && scene_tree->get_rect().has_point(scene_tree->get_local_mouse_position())) {
			tree_clicked = true;
		} else if (!mb->is_pressed()) {
			tree_clicked = false;
		}
		if (!mb->is_pressed() && pending_click_select) {
			_push_item(pending_click_select);
			pending_click_select = nullptr;
		}
	}
}
void SceneTreeDock::shortcut_input(const Ref<InputEvent> &p_event) {