### 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)

EditorProgress ep("savepack", TTR("Packing"), 102, true);
	
	Ref<DirAccess> da = DirAccess::create(DirAccess::ACCESS_FILESYSTEM);
	da->make_dir_recursive(EditorPaths::get_singleton()->get_cache_dir());
	String tmppath = EditorPaths::get_singleton()->get_cache_dir().path_join("packtmp");
	Ref<FileAccess> ftmp = FileAccess::open(tmppath, FileAccess::WRITE);
	if (ftmp.is_null()) {
		add_message(EXPORT_MESSAGE_ERROR, TTR("Save PCK"), vformat(TTR("Cannot create file \"%s\"."), tmppath));
		return ERR_CANT_CREATE;
	}
	PackData pd;
	pd.ep = &ep;
	pd.f = ftmp;
	pd.so_files = p_so_files;
	Error err = export_project_files(p_preset, p_debug, _save_pack_file, &pd, _add_shared_object);
	
	pd.f.unref();
	ftmp.unref();
	if (err != OK) {
		DirAccess::remove_file_or_error(tmppath);
		add_message(EXPORT_MESSAGE_ERROR, TTR("Save PCK"), TTR("Failed to export project files."));
		return err;
	}
	pd.file_ofs.sort(); 
	Ref<FileAccess> f;
	int64_t embed_pos = 0;
	if (!p_embed) {
		
		f = FileAccess::open(p_path, FileAccess::WRITE);