### 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)

manifest["name"] = proj_name;
	manifest["start_url"] = "./" + name + ".html";
	manifest["display"] = String::utf8(modes[display]);
	manifest["orientation"] = String::utf8(orientations[orientation]);
	manifest["background_color"] = "#" + p_preset->get("progressive_web_app/background_color").operator Color().to_html(false);
	Array icons_arr;
	const String icon144_path = p_preset->get("progressive_web_app/icon_144x144");
	err = _add_manifest_icon(p_path, icon144_path, 144, icons_arr);
	if (err != OK) {
		return err;
	}
	const String icon180_path = p_preset->get("progressive_web_app/icon_180x180");
	err = _add_manifest_icon(p_path, icon180_path, 180, icons_arr);
	if (err != OK) {
		return err;
	}
	const String icon512_path = p_preset->get("progressive_web_app/icon_512x512");
	err = _add_manifest_icon(p_path, icon512_path, 512, icons_arr);
	if (err != OK) {
		return err;
	}
	manifest["icons"] = icons_arr;
	CharString cs = Variant(manifest).to_json_string().utf8();
	err = _write_or_error((const uint8_t *)cs.get_data(), cs.length(), dir.path_join(name + ".manifest.json"));
	if (err != OK) {
		return err;
	}
	return OK;
}
void EditorExportPlatformWeb::get_preset_features(const Ref<EditorExportPreset> &p_preset, List<String> *r_features) const {