### 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)

hide();
	EditorNode::get_singleton()->open_export_template_manager();
}
void ProjectExportDialog::_validate_export_path(const String &p_path) {
	
	bool invalid_path = (p_path.get_file().get_basename().is_empty());
	
	if (invalid_path && export_project->get_ok_button()->is_disabled()) {
		return;
	}
	if (!invalid_path && !export_project->get_ok_button()->is_disabled()) {
		return;
	}
	if (invalid_path) {
		export_project->get_ok_button()->set_disabled(true);
		export_project->get_line_edit()->disconnect("text_submitted", callable_mp(export_project, &EditorFileDialog::_file_submitted));
	} else {
		export_project->get_ok_button()->set_disabled(false);
		export_project->get_line_edit()->connect("text_submitted", callable_mp(export_project, &EditorFileDialog::_file_submitted));
	}
}
void ProjectExportDialog::_export_project() {