### 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)

export_filter->add_item(TTR("Export selected resources (and dependencies)"));
	export_filter->add_item(TTR("Export all resources in the project except resources checked below"));
	export_filter->add_item(TTR("Export as dedicated server"));
	resources_vb->add_margin_child(TTR("Export Mode:"), export_filter);
	export_filter->connect("item_selected", callable_mp(this, &ProjectExportDialog::_export_type_changed));
	include_label = memnew(Label);
	include_label->set_text(TTR("Resources to export:"));
	resources_vb->add_child(include_label);
	include_margin = memnew(MarginContainer);
	include_margin->set_v_size_flags(Control::SIZE_EXPAND_FILL);
	resources_vb->add_child(include_margin);
	include_files = memnew(Tree);
	include_margin->add_child(include_files);
	include_files->connect("item_edited", callable_mp(this, &ProjectExportDialog::_tree_changed));
	include_files->connect("check_propagated_to_item", callable_mp(this, &ProjectExportDialog::_check_propagated_to_item));
	include_files->connect("custom_popup_edited", callable_mp(this, &ProjectExportDialog::_tree_popup_edited));
	server_strip_message = memnew(Label);
	server_strip_message->set_visible(false);
	server_strip_message->set_autowrap_mode(TextServer::AUTOWRAP_WORD_SMART);
	resources_vb->add_child(server_strip_message);
	{
		List<StringName> resource_names;
		ClassDB::get_inheriters_from_class("Resource", &resource_names);
		PackedStringArray strippable;
		for (StringName resource_name : resource_names) {
			if (ClassDB::has_method(resource_name, "create_placeholder", true)) {
				strippable.push_back(resource_name);
			}
		}
		strippable.sort();