The muffins were rock hard, what did I do wrong?

What makes muffins soft is starch and fat. You have no fat at all in these "muffins", and very little flour when compared to the vegetables and proteins.

Normal muffin proportions are 2:2:1:1 flour:liquid:egg:fat (per Ruhlmann). I guess you can add up to 2 parts filler (so as much vegetable as flour) before you get the result too terrible. In your mixture, there is a total of 140 g flour and ~700 g fillers (bran, beans, whey, carrots, bananas). This is never going to be muffin-like, you will have to forgo most of your additions. And the whole wheat flour is also making it harder. You either have to change to normal flour, or live with some hardness (it should be manageable if you change all the other factors).

The liquid provided by the yogurt is good if you switch to white flour, no need to change anything there. You may consider adding a bit if you stay with whole wheat, it "soaks" more liquid.

The egg whites are a problem too. First, egg whites make baked goods dry out. You shouldn't be using pure egg whites, they will make bad muffins. You need whole eggs. And second, the equivalent of 4 eggs (200 gram) is probably too much. 1-2 whole eggs would be normal for this amount of flour, 3 makes it pound-cake-like but still usable. Still, you may find out that, if you make all the other changes, upping the (whole) eggs to 4 doesn't make it too bad.

You also used too little sugar. Sugar is an important structural element in muffins. It retains moisture and prevents gluten buildup. It can be reduced if you don't want the taste or the calories, but each gram you take away also reduces the quality of the muffin, so you have to try out and see how much quality reduction you can tolerate.

You had absolutely no fat in the recipe. The standard ratio suggests 75 g. This is also a major factor in softness and moisture.

In short, you cannot take any muffin recipe, remove all the stuff which doesn't have the nutrients you don't want, fill it up with foodstuff you want, pour it into a muffin form and expect it to taste like a muffin. Baking is chemically very complicated, and most of the ingredients are not there for flavor, but for texture. Replacing them with random other ingredients will do nothing good.

You can either return your recipe towards a more traditional muffin, which will of course change its nutrition values back to "sweet baked good", or you can find a different form of combining the foodstuff you have chosen to eat. Mixing it and baking it is not going to work.

Here's a few problems I see:

1. Too many vegetables: You don't need to clean out your refrigerator to make muffins. Pick either a cup of carrots, or bananas, or mung beans, but not all three with one cup of each.

2. Not enough gluten: You've got oats and millet contributing no gluten, and whole wheat flour contributing very little, then just 40g of all-purpose to build the entire structure. With the weight of all the vegetation, it's no surprise they couldn't hold up. Replace more of the low-gluten flours with all purpose, or bread flour (1:1 is as high as I would go, and 2:1 all purpose:others is better).

3. Not enough leavening: 2 tsp of baking soda is good for about a dozen small-medium muffins. It looks like you're making 2 dozen, or very big ones. The egg whites won't help much unless you whip them up first, and even then the air will come up when you add the heavy stuff. Try whole eggs instead, and adjust baking soda/add baking powder based on the next point...

4. Acidic pH: Both whey and yogurt are acidic (as are eggs, but it might be in the yolks), and the amounts you put in won't be counteracted by the amount of baking soda, so your recipe will be net acidic. This affects the leavening ability of baking soda, and will harm yeast if you want to use that (unless it's a sourdough starter). I would cut out the yogurt, consider adding more baking soda, and then add neutral baking powder once you think the pH balance is ok.