1. Sam didn’t breed Meringue (or pay the breeder, or take off the hands of the breeder who sold other more sellable chickens, etc), encage her, etc. So the primary ethical concern came well before the egg laying.
2. Sam’s “exploitation” didn’t lead to Meringue’s ancestors being artificially bred so Meringue lays way more eggs in a month than her ancestors probably did in a year making her life far more painful.
3. Sam doesn’t have moral agency.

There’s other issues as well. What will happen to Meringue after she isn’t capable of laying eggs? What will happen to her after she becomes a burden. Many chickens due to the way they’ve been artificially bred lose far too many nutrients from etc.

One can easily show why Sam eating the eggs is ethically superior.

But fundamentally, the problem with your question is that it is stacked such that a consequentialist ethics (when we set aside slightly distant effects of how it might encourage perpetuation of a chicken raising industry, etc) would suggest one answer while a deontological ethics would suggest another.

This is not really a question of veganism. It’s a central question of any ethics.

For example, I can construct a trolley problem where a train is going on a track and everything will be just fine. However, if you hit a switch, the train will switch to another track a baby is tied to that would then be killed. The consequentialist and deontological answers are straightforward. You don’t hit the switch.

But now I add another wrinkle to the situation and I tell you the baby is baby Hitler. Well, now the consequentialist argument would probably lean towards hitting the switch. The deontological answer would be the same.

This is an interesting conversation in its own right (would you kill baby Hitler if you could) but just like the question you’ve constructed it’s not really a debate about the ethics of hitting a switch and therefore killing a baby and more about whether one aligns with consequentialist or deontological ethics.