### 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
return scene_tabs->get_current_tab();
}
void EditorSceneTabs::_bind_methods() {
	ADD_SIGNAL(MethodInfo("tab_changed", PropertyInfo(Variant::INT, "tab_index")));
	ADD_SIGNAL(MethodInfo("tab_closed", PropertyInfo(Variant::INT, "tab_index")));
	ClassDB::bind_method("_tab_preview_done", &EditorSceneTabs::_tab_preview_done);
}
EditorSceneTabs::EditorSceneTabs() {
	singleton = this;
	set_process_shortcut_input(true);
	tabbar_panel = memnew(PanelContainer);
	add_child(tabbar_panel);
	tabbar_container = memnew(HBoxContainer);
	tabbar_panel->add_child(tabbar_container);
	scene_tabs = memnew(TabBar);
	scene_tabs->set_select_with_rmb(true);
	scene_tabs->add_tab("unsaved");
	scene_tabs->set_tab_close_display_policy((TabBar::CloseButtonDisplayPolicy)EDITOR_GET("interface/scene_tabs/display_close_button").operator int());
	scene_tabs->set_max_tab_width(int(EDITOR_GET("interface/scene_tabs/maximum_width")) * EDSCALE);
	scene_tabs->set_drag_to_rearrange_enabled(true);
	scene_tabs->set_auto_translate(false);
	scene_tabs->set_h_size_flags(Control::SIZE_EXPAND_FILL);
	tabbar_container->add_child(scene_tabs);
	scene_tabs->connect("tab_changed", callable_mp(this, &EditorSceneTabs::_scene_tab_changed));
	scene_tabs->connect("tab_button_pressed", callable_mp(this, &EditorSceneTabs::_scene_tab_script_edited));
	scene_tabs->connect("tab_close_pressed", callable_mp(this, &EditorSceneTabs::_scene_tab_closed));
	scene_tabs->connect("tab_hovered", callable_mp(this, &EditorSceneTabs::_scene_tab_hovered));
	scene_tabs->connect("mouse_exited", callable_mp(this, &EditorSceneTabs::_scene_tab_exit));
	scene_tabs->connect("gui_input", callable_mp(this, &EditorSceneTabs::_scene_tab_input));