### 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 project file dialog.
	export_project = memnew(EditorFileDialog);
	export_project->set_access(EditorFileDialog::ACCESS_FILESYSTEM);
	add_child(export_project);
	export_project->connect("file_selected", callable_mp(this, &ProjectExportDialog::_export_project_to_path));
	export_project->get_line_edit()->connect("text_changed", callable_mp(this, &ProjectExportDialog::_validate_export_path));
	export_debug = memnew(CheckBox);
	export_debug->set_text(TTR("Export With Debug"));
	export_debug->set_pressed(true);
	export_debug->set_h_size_flags(Control::SIZE_SHRINK_CENTER);
	export_project->get_vbox()->add_child(export_debug);
	export_pck_zip_debug = memnew(CheckBox);
	export_pck_zip_debug->set_text(TTR("Export With Debug"));
	export_pck_zip_debug->set_pressed(true);
	export_pck_zip_debug->set_h_size_flags(Control::SIZE_SHRINK_CENTER);
	export_pck_zip->get_vbox()->add_child(export_pck_zip_debug);
	set_hide_on_ok(false);
	default_filename = EditorSettings::get_singleton()->get_project_metadata("export_options", "default_filename", "");
	// If no default set, use project name
	if (default_filename.is_empty()) {
		// If no project name defined, use a sane default
		default_filename = GLOBAL_GET("application/config/name");
		if (default_filename.is_empty()) {
			default_filename = "UnnamedProject";
		}
	}
}
ProjectExportDialog::~ProjectExportDialog() {
}