### 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)

const char **aperms = android_perms;
	while (*aperms) {
		bool enabled = p_preset->get("permissions/" + String(*aperms).to_lower());
		if (enabled) {
			r_permissions.push_back("android.permission." + String(*aperms));
		}
		aperms++;
	}
	PackedStringArray user_perms = p_preset->get("permissions/custom_permissions");
	for (int i = 0; i < user_perms.size(); i++) {
		String user_perm = user_perms[i].strip_edges();
		if (!user_perm.is_empty()) {
			r_permissions.push_back(user_perm);
		}
	}
	if (p_give_internet) {
		if (r_permissions.find("android.permission.INTERNET") == -1) {
			r_permissions.push_back("android.permission.INTERNET");
		}
	}
}
void EditorExportPlatformAndroid::_write_tmp_manifest(const Ref<EditorExportPreset> &p_preset, bool p_give_internet, bool p_debug) {
	print_verbose("Building temporary manifest...");
	String manifest_text =
			"<?xml version=\"1.0\" encoding=\"utf-8\"?>\n"
			"<manifest xmlns:android=\"http://schemas.android.com/apk/res/android\"\n"
			"    xmlns:tools=\"http://schemas.android.com/tools\">\n";
	manifest_text += _get_screen_sizes_tag(p_preset);
	manifest_text += _get_gles_tag();
	Vector<String> perms;