### 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)

if (abi_index != -1) {
			exported = true;
			String base = "res://android/build/libs";
			String type = export_data->debug ? "debug" : "release";
			String abi = abis[abi_index].abi;
			String filename = p_so.path.get_file();
			String dst_path = base.path_join(type).path_join(abi).path_join(filename);
			Vector<uint8_t> data = FileAccess::get_file_as_bytes(p_so.path);
			print_verbose("Copying .so file from " + p_so.path + " to " + dst_path);
			Error err = store_file_at_path(dst_path, data);
			ERR_FAIL_COND_V_MSG(err, err, "Failed to copy .so file from " + p_so.path + " to " + dst_path);
			export_data->libs.push_back(dst_path);
		}
	}
	ERR_FAIL_COND_V_MSG(!exported, FAILED,
			"Cannot determine architecture for library \"" + p_so.path + "\". One of the supported architectures must be used as a tag:" + join_abis(abis, " ", true));
	return OK;
}
bool EditorExportPlatformAndroid::_has_read_write_storage_permission(const Vector<String> &p_permissions) {
	return p_permissions.find("android.permission.READ_EXTERNAL_STORAGE") != -1 || p_permissions.find("android.permission.WRITE_EXTERNAL_STORAGE") != -1;
}
bool EditorExportPlatformAndroid::_has_manage_external_storage_permission(const Vector<String> &p_permissions) {
	return p_permissions.find("android.permission.MANAGE_EXTERNAL_STORAGE") != -1;
}
bool EditorExportPlatformAndroid::_uses_vulkan() {
	String current_renderer = GLOBAL_GET("rendering/renderer/rendering_method.mobile");
	bool uses_vulkan = (current_renderer == "forward_plus" || current_renderer == "mobile") && GLOBAL_GET("rendering/rendering_device/driver.android") == "vulkan";
	return uses_vulkan;
}
void EditorExportPlatformAndroid::_get_permissions(const Ref<EditorExportPreset> &p_preset, bool p_give_internet, Vector<String> &r_permissions) {