### 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)

_get_permissions(p_preset, p_give_internet, perms);
	for (int i = 0; i < perms.size(); i++) {
		String permission = perms.get(i);
		if (permission == "android.permission.WRITE_EXTERNAL_STORAGE" || (permission == "android.permission.READ_EXTERNAL_STORAGE" && _has_manage_external_storage_permission(perms))) {
			manifest_text += vformat("    <uses-permission android:name=\"%s\" android:maxSdkVersion=\"29\" />\n", permission);
		} else {
			manifest_text += vformat("    <uses-permission android:name=\"%s\" />\n", permission);
		}
	}
	if (_uses_vulkan()) {
		manifest_text += "    <uses-feature tools:node=\"replace\" android:name=\"android.hardware.vulkan.level\" android:required=\"false\" android:version=\"1\" />\n";
		manifest_text += "    <uses-feature tools:node=\"replace\" android:name=\"android.hardware.vulkan.version\" android:required=\"true\" android:version=\"0x400003\" />\n";
	}
	Vector<Ref<EditorExportPlugin>> export_plugins = EditorExport::get_singleton()->get_export_plugins();
	for (int i = 0; i < export_plugins.size(); i++) {
		if (export_plugins[i]->supports_platform(Ref<EditorExportPlatform>(this))) {
			const String contents = export_plugins[i]->get_android_manifest_element_contents(Ref<EditorExportPlatform>(this), p_debug);
			if (!contents.is_empty()) {
				manifest_text += contents;
				manifest_text += "\n";
			}
		}
	}
	manifest_text += _get_application_tag(Ref<EditorExportPlatform>(this), p_preset, _has_read_write_storage_permission(perms), p_debug);
	manifest_text += "</manifest>\n";
	String manifest_path = vformat("res://android/build/src/%s/AndroidManifest.xml", (p_debug ? "debug" : "release"));
	print_verbose("Storing manifest into " + manifest_path + ": " + "\n" + manifest_text);
	store_string_at_path(manifest_path, manifest_text);
}
void EditorExportPlatformAndroid::_fix_manifest(const Ref<EditorExportPreset> &p_preset, Vector<uint8_t> &p_manifest, bool p_give_internet) {