I use "fresh" eggs for all cooking and baking.
All my recipes use the eggs cold.

I try to use all eggs within about a week from supermarket purchase.

When an egg floats it's time to bury it.

After a while in the refrigerator the egg degrades to a point at which
it may still be edible but almost impossible to use for fried eggs
without the yolk breaking.

I have only used eggs as a binder when used with other ingredients,
like making a meatloaf. Whole egg, cold from refrigerator , beaten with
a tiny bit of milk.