Yes, it's not an egg. It could also be trash.I could see a bee carrying something white in your video. If it was an egg it would be too small to see. Could it be white pollen?
With the brood box getting full they may be looking for space to put more pollen. I'd believe they were eggs if you could lift out the FlowHive cassette and photograph eggs and larvae in the cells. Is that even possible with a FlowHive?
The workers lay them. Every hive has laying workers. Usually the house bees eat them.