Poweramp casts audio directly from your phone/tablet (where Poweramp app runs). This means your device should be able to connect to the Chromecast device and also Chromecast device should be able to connect to your phone/tablet.
In case it doesn't work:
- ensure you have Chromecast firmware / Chromecast receiver app (Google TV/Android TV) updated
- you don't have "Isolated clients" or similarly named router options enabled
- if you have firewall on the device, it allows inbound connections from within your network on ports 18888-18988
- you're able to connect to https://powerampapp.com from within your network