With limits on eggs now I thought it might be good to post some substitutes and notes on what has worked vs what was not that great.
For scrambled eggs and quiche I used to use silken tofu. It wasn’t that pretty and didn’t taste quite the same, but I seasoned it with soy sauce and didn’t die. If you’re willing to buy a niche product black salt contains sulfur and will give an eggy taste.
Mashed banana and applesauce are often recommended - I forget if I’ve tried them.
Yogurt was used as a substitute in muffins but I didn’t like the result much. It made them a little dense and heavy. Perhaps it was that I used plain Greek yogurt rather than a thinner variety, plus muffins are supposed to be especially light.
Blancmange is egg free, made using cornstarch, and can be eaten instead of custard. (Though blancmange is usually served cold and set like jelly rather than as a hot dish/sauce)
There are egg free cake and biscuit recipes out there too.
Egg replacer powders are a thing but are more for baking rather than egg-based dishes.
Yogurt, mayo or sour cream can be use instead of egg when crumbing meat or veg.
Milk can be used instead of an egg wash for scones or pastry.
Whey powder and aquafaba are also useful as substitutes.