Stryd is compatible with the Zwift app. When you pair Stryd to the Zwift app, the app will only use distance, pace, and cadence from Stryd. You will still be able to see your data in PowerCenter after the run by offline syncing your Stryd.
Note that Zwift uses Bluetooth to connect to your Stryd. This means you must unpair your phone from Stryd since it only supports one bluetooth connection at a time.