I gave the two turtles seaweed and they mated, but no eggs were laid, just a baby was born, like pigs or cows.
Can this be due to the server I'm playing on or is it a bug?
If you pair the turtles yourself, then the little one will appear directly! You can only place the eggs yourself to breed them. By mating yourself, none of the animals will lay any egg. Which at the moment i think is only the case with the toads
Turtles don't drop babies when paired, they always lay eggs.
"Turtle eggs can be farmed by https://minecraft.fandom.com/wiki/Breeding turtles. When two turtles close to each other are fed https://minecraft.fandom.com/wiki/Seagrass, one of them will burrow into nearby https://minecraft.fandom.com/wiki/Sand and lay 1-4 eggs".
https://minecraft.fandom.com/wiki/Turtle_Egg
But here I'm told something else.
That sounds really weird, can you reproduce it? What version are you playing in?
Happens again and again. The server runs on 1.14.
Funny. Take a closer look, maybe with a higher version.