### Tested versions

Godot Engine v4.2.stable.official.46dc27791

### System information

Windows 10

### Issue description

When exporting to web, Godot fails with this error in the console:

> scene/main/window.cpp:884 - Attempting to make child window exclusive, but the parent window already has another exclusive child. This window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->VBoxContainer@<!-- -->137/@<!-- -->AcceptDialog@<!-- -->411, parent window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559, current exclusive child window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->ProgressDialog@<!-- -->17444

![a](https://github.com/godotengine/godot/assets/2000051/bf9d22aa-d3fe-4e11-bff6-c387e740fe90)

This happens for newly created empty projects.


### Steps to reproduce

1. Open the attached project (or create a new project).
2. Project->Export->Export All
3. Observe the console error.  No output files are generated.


### Minimal reproduction project (MRP)

[export_test.zip](https://github.com/godotengine/godot/files/13574810/export_test.zip)

if (show_dialog) {
		result_dialog->popup_centered_ratio(0.5);
	}
	exporting = false;
}
void ProjectExportDialog::_bind_methods() {
	ClassDB::bind_method("_export_all", &ProjectExportDialog::_export_all);
	ClassDB::bind_method("set_export_path", &ProjectExportDialog::set_export_path);
	ClassDB::bind_method("get_export_path", &ProjectExportDialog::get_export_path);
	ClassDB::bind_method("get_current_preset", &ProjectExportDialog::get_current_preset);
	ADD_PROPERTY(PropertyInfo(Variant::STRING, "export_path"), "set_export_path", "get_export_path");
}
ProjectExportDialog::ProjectExportDialog() {
	set_title(TTR("Export"));
	set_clamp_to_embedder(true);
	VBoxContainer *main_vb = memnew(VBoxContainer);
	add_child(main_vb);
	HSplitContainer *hbox = memnew(HSplitContainer);
	main_vb->add_child(hbox);
	hbox->set_v_size_flags(Control::SIZE_EXPAND_FILL);
	
	VBoxContainer *preset_vb = memnew(VBoxContainer);
	preset_vb->set_h_size_flags(Control::SIZE_EXPAND_FILL);
	hbox->add_child(preset_vb);
	Label *l = memnew(Label(TTR("Presets")));
	l->set_theme_type_variation("HeaderSmall");
	HBoxContainer *preset_hb = memnew(HBoxContainer);
	preset_hb->add_child(l);
	preset_hb->add_spacer();
	preset_vb->add_child(preset_hb);