In recent times, air play has helped tremendously, but there seems to still be issues with connectivity and sound at times. A great advancement though considering the past.
Apple products dont support screen mirroring (Miracast), but they do support Airplay2 mirroring.
Its not clear what RokuOS firmware version/build you are on, however, version 10 has significant AirPlay component updates - check to see if its available for you: Settings/System/System update/Check now
If its not, be assured that when version 10 does rollout for you, it will likely improve such issues.