### Godot version

4.2 dev4

### System information

Windows 10.0.19045 - Vulkan (Forward+) - dedicated NVIDIA GeForce GTX 1060 (NVIDIA; 30.0.15.1403) - Intel(R) Core(TM) i7-7700HQ CPU @ 2.80GHz (8 Threads)

### Issue description

When you have many tabs opened and they are overflowing with the < > buttons, when you switch scene tab it may hide some tabs in specific circumstances:

https://github.com/godotengine/godot/assets/2223172/e5904497-6e3f-48af-815a-3a156ca15018

I'd expect that simply switching to another tab has no effect on visibility.

### Steps to reproduce

1. Open many scene tabs
2. Repeat what I did on the video
May depend on tab names and window size.

### Minimal reproduction project

N/A
if (OS::get_singleton()->get_main_loop()) {
		List<String> args;
		args.push_back("-p");
		OS::get_singleton()->create_instance(args);
	}
}
void EditorSceneTabs::shortcut_input(const Ref<InputEvent> &p_event) {
	ERR_FAIL_COND(p_event.is_null());
	Ref<InputEventKey> k = p_event;
	if ((k.is_valid() && k->is_pressed() && !k->is_echo()) || Object::cast_to<InputEventShortcut>(*p_event)) {
		if (ED_IS_SHORTCUT("editor/next_tab", p_event)) {
			int next_tab = EditorNode::get_editor_data().get_edited_scene() + 1;
			next_tab %= EditorNode::get_editor_data().get_edited_scene_count();
			_scene_tab_changed(next_tab);
		}
		if (ED_IS_SHORTCUT("editor/prev_tab", p_event)) {
			int next_tab = EditorNode::get_editor_data().get_edited_scene() - 1;
			next_tab = next_tab >= 0 ? next_tab : EditorNode::get_editor_data().get_edited_scene_count() - 1;
			_scene_tab_changed(next_tab);
		}
	}
}
void EditorSceneTabs::add_extra_button(Button *p_button) {
	tabbar_container->add_child(p_button);
}
void EditorSceneTabs::set_current_tab(int p_tab) {
	scene_tabs->set_current_tab(p_tab);
}
int EditorSceneTabs::get_current_tab() const {