Making how much batter will result in over-mixing?

The amount is only restricted by the capacity of the tools you have at hand. The point is, don't mix too much. If you have a bowl, filled to the brim, you will have to mix a lot more to get all of the ingredients incorporated. If that same bowl is half full, a few quick strokes is all it takes to mix. Over-mixing risks building the gluten structure too much, which results in a "tougher", less light, final product. Bakeries, restaurants, and catering services probably do more at once than most people do at home...it is just that they have larger capacity tools.

The question in your title has no answer, even though the information you found is, by itself, correct.

The article is correct in that, when attempting to make too large batches of cake batter, you may paint yourself into a corner where you have no other options but to overmix. But in reality, there is no strict "if you do X, you will certainly overmix, if you do Y, you will certainly not overmix" border - and the site is not claiming that there is either, they just suggest to make each cake layer separately, to reduce the potential for introducing mixing problems.

The best guideline I can give you is sadly vague: if you find that you have to add flour in more than three batches, with an acceptable amount of mixing per batch, then you are making too much batter at once. This makes it dependent on many factors:

• The exact cake recipe
• How "willingly" the batter takes in the flour you are stirring in
• What size tools you have. With an industrial-sized mixer, you could probably sieve a kilogram of flour over an egg mixture and have it stirred in with 3-4 slow turns of the paddle.
• Your experience as a baker. The better you are at incorporating flour, the more batter you can make at once without problems. Also, it is what allows you to recognize what amount of mixing per batch is "acceptable" while you observe how the batter acts to the flour addition.

A much more practicable idea is to do exactly what the site suggests that you do: follow the recipe you have without doubling it. A good recipe has been tested to work, without overmixing or other problems. If it is a recipe for a single layer, mix your cake one layer at a time.

The whole article is about cakes. It doesn't apply to crepe batters.

For a cake made with flour:sugar:sunflower oil:milk 1:1:1:1, I wouldn't worry about optimal mixing. Such a cake won't give you an especially fine texture anyway, and you won't notice the effects of minimal mixing in it. And you likely want it to develop a bit of gluten too, because it has no eggs to hold it together. Just dump everything into the bowl, mix until smooth, and bake away (muffin method). You might want to stir the leavener into the flour first, to avoid it from clumping.