Hey there,
It sounds like your connection is being interrupted partially and that is causing the desync. This forum post has more information about this type of desync in Hearthstone.
If possible try swapping to a direct wired connection to your router, to rule out any wi-fi issues that might be causing it. If it’s still happening after using an ethernet connection it may be an issue with your router or internet provider. You may try testing an alternate connection, such as a mobile data hotspot or VPN temporarily, to see if the issue stops.