### 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 (p_index < 0 || p_index >= presets->get_item_count()) {
		name->set_text("");
		name->set_editable(false);
		export_path->hide();
		runnable->set_disabled(true);
		parameters->edit(nullptr);
		presets->deselect_all();
		duplicate_preset->set_disabled(true);
		delete_preset->set_disabled(true);
		sections->hide();
		export_error->hide();
		export_templates_error->hide();
		return;
	}
	Ref<EditorExportPreset> current = EditorExport::get_singleton()->get_export_preset(p_index);
	ERR_FAIL_COND(current.is_null());
	updating = true;
	presets->select(p_index);
	sections->show();