### 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)

add_preset = memnew(MenuButton);
	add_preset->set_text(TTR("Add..."));
	add_preset->get_popup()->connect("index_pressed", callable_mp(this, &ProjectExportDialog::_add_preset));
	preset_hb->add_child(add_preset);
	MarginContainer *mc = memnew(MarginContainer);
	preset_vb->add_child(mc);
	mc->set_v_size_flags(Control::SIZE_EXPAND_FILL);
	presets = memnew(ItemList);
	SET_DRAG_FORWARDING_GCD(presets, ProjectExportDialog);
	mc->add_child(presets);
	presets->connect("item_selected", callable_mp(this, &ProjectExportDialog::_edit_preset));
	duplicate_preset = memnew(Button);
	duplicate_preset->set_tooltip_text(TTR("Duplicate"));
	duplicate_preset->set_flat(true);
	preset_hb->add_child(duplicate_preset);
	duplicate_preset->connect("pressed", callable_mp(this, &ProjectExportDialog::_duplicate_preset));
	delete_preset = memnew(Button);
	delete_preset->set_tooltip_text(TTR("Delete"));
	delete_preset->set_flat(true);
	preset_hb->add_child(delete_preset);
	delete_preset->connect("pressed", callable_mp(this, &ProjectExportDialog::_delete_preset));
	
	VBoxContainer *settings_vb = memnew(VBoxContainer);
	settings_vb->set_h_size_flags(Control::SIZE_EXPAND_FILL);
	hbox->add_child(settings_vb);
	name = memnew(LineEdit);
	settings_vb->add_margin_child(TTR("Name:"), name);
	name->connect("text_changed", callable_mp(this, &ProjectExportDialog::_name_changed));
	runnable = memnew(CheckButton);
	runnable->set_text(TTR("Runnable"));