Do honey bee eggs just sit in the cell and do nothing?
It’s is hard to image what you expect them to do. I’ve never seen an industrious-looking egg, even though a lot is happening on the inside.
Honey bees remain in the egg stage for about 72-76 hours, assuming nest temperatures are normal. During that time, the fertilized (female) or unfertilized (male) cells begin dividing and differentiating into the tissues that will form a larva. This is a complex process that is not visible from the outside.
After the third day, the egg ecloses into a larva. The term “eclose” is used because the larva doesn’t “hatch” like a chicken does. Instead, the outer covering of the egg just dissolves away, which is why you never see egg shells in the bottom of your brood comb.
So, in answer to your question, rather than doing “nothing,” your honey bee eggs are actively growing into larvae.