You can only connect Stryd to one BT device. I believe that Zwift connects to Stryd via BT which will prevent the AW Stryd app connecting to the pod.
I connect my Treadmill (Techongyn Myrun) directly to zwift via BT and my Stryd pod to AW Ultra via BT. Hit start on both the TM and AW Stryd app within a couple of seconds of each other. Works ok. This allows me to compare the TM speed & cadence with Stryd speed and cadence while running.
Zwift does not display incline. When doing a zwift structured workout the runner will be instructed via on-screen text when to set the incline and by how much, but there is no provision for displaying it in-game… The AW Stryd app allows manual input of incline if the Treadmill Workout Profile was selected.