### 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)

runnable->set_tooltip_text(TTR("If checked, the preset will be available for use in one-click deploy.\nOnly one preset per platform may be marked as runnable."));
	runnable->connect("pressed", callable_mp(this, &ProjectExportDialog::_runnable_pressed));
	settings_vb->add_child(runnable);
	export_path = memnew(EditorPropertyPath);
	settings_vb->add_child(export_path);
	export_path->set_label(TTR("Export Path"));
	export_path->set_object_and_property(this, "export_path");
	export_path->set_save_mode();
	export_path->connect("property_changed", callable_mp(this, &ProjectExportDialog::_export_path_changed));
	
	sections = memnew(TabContainer);
	sections->set_use_hidden_tabs_for_min_size(true);
	sections->set_theme_type_variation("TabContainerOdd");
	settings_vb->add_child(sections);
	sections->set_v_size_flags(Control::SIZE_EXPAND_FILL);
	
	parameters = memnew(EditorInspector);
	sections->add_child(parameters);
	parameters->set_name(TTR("Options"));
	parameters->set_v_size_flags(Control::SIZE_EXPAND_FILL);
	parameters->set_use_doc_hints(true);
	parameters->connect("property_edited", callable_mp(this, &ProjectExportDialog::_update_parameters));
	EditorExport::get_singleton()->connect("export_presets_updated", callable_mp(this, &ProjectExportDialog::_force_update_current_preset_parameters));
	
	VBoxContainer *resources_vb = memnew(VBoxContainer);
	sections->add_child(resources_vb);
	resources_vb->set_name(TTR("Resources"));
	export_filter = memnew(OptionButton);
	export_filter->add_item(TTR("Export all resources in the project"));
	export_filter->add_item(TTR("Export selected scenes (and dependencies)"));