### 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)

return "Web";
}
String EditorExportPlatformWeb::get_os_name() const {
	return "Web";
}
Ref<Texture2D> EditorExportPlatformWeb::get_logo() const {
	return logo;
}
bool EditorExportPlatformWeb::has_valid_export_configuration(const Ref<EditorExportPreset> &p_preset, String &r_error, bool &r_missing_templates, bool p_debug) const {
#ifdef MODULE_MONO_ENABLED
	
	r_error += TTR("Exporting to Web is currently not supported in Godot 4 when using C#/.NET. Use Godot 3 to target Web with C#/Mono instead.") + "\n";
	r_error += TTR("If this project does not use C#, use a non-C# editor build to export the project.") + "\n";
	return false;
#else
	String err;
	bool valid = false;
	bool extensions = (bool)p_preset->get("variant/extensions_support");
	
	bool dvalid = exists_export_template(_get_template_name(extensions, true), &err);
	bool rvalid = exists_export_template(_get_template_name(extensions, false), &err);
	if (p_preset->get("custom_template/debug") != "") {
		dvalid = FileAccess::exists(p_preset->get("custom_template/debug"));
		if (!dvalid) {
			err += TTR("Custom debug template not found.") + "\n";
		}