Unsweetened applesauce is my go to egg replacement for things like cookies and brownies that only need the emulsifying properties. 1/4-1/3 cup per egg works nearly perfectly for things that call for 1-2 eggs. Beyond that the consistency gets a bit off, but it's usually still good enough.

I mostly recall arrowroot powder as being an alternative thickener for water-based stuff, so an alternative to cornstarch or flour.

With breads, egg is mostly a binder, as I recall, help keep things together. Like, if one doesn't have it, you'd expect the thing to be crumbly. I'd think of something like vital wheat gluten to fill that role.

kagis

Hmm. This has people testing various egg substitutes, and they do indeed have arrowroot powder on there.

https://www.thekitchn.com/best-egg-substitutes-baking-23003895

Substitute #4: Arrowroot Powder

Replacement : 2 tablespoons arrowroot powder and 3 tablespoons water = 1 large egg

Rating: 3/10

Arrowroot comes from a tuber in South America and can be used in everything from gravies to pies to thicken liquids. As an egg replacement for baking, arrowroot is mixed with water to form a slurry before being added to the muffin mixture. In this simple muffin recipe, the arrowroot brought out some extra sweetness, but left the muffins a bit dry.

I guess it can indeed work.