You can not use Zwift + Stryd at the same time as a Stryd Treadmill Workout if you use Bluetooth to connect Zwift to your Stryd device (which is the most typical way people use Zwift). The Stryd mobile app connects to the Stryd pod via Bluetooth. The Stryd pod only has the capability to connect to one Bluetooth device at a time. This means that there will not be a Bluetooth signal for Zwift to use to connect to Stryd.
However, for users that are able to connect Stryd to Zwift via ANT, they could use the Stryd Treadmill Workout app at the same time as Zwift + Stryd. The ANT Zwift connection often requires an external ANT Dongle. You can learn more about using Zwift via ANT on the Zwift: https://support.zwift.com/en_us/ant-and-ble-overview-H1FrT2zwH