I prefer egg-yolk gnocchi but I’ve been successful in making yolk-free, pillowy, fluffy gnocchi by subbing out a couple of the russets (~1/5 the total weight of the potatoes) with yams or sweet potatoes in combination with my own invention that my spouse calls it “yuck yolk” because it looks like pet vomit. It's a combo of finely ground flax or ground chia seed soaked in a little aquafaba. The high Omega 3 content of flax can impart a fishy flavor so don’t overdo it.
The resulting gray mush should have a pudding-like texture. I lay riced potatoes on a cookie sheet as soon as they’re baked to let the steam out of them.
Then I sprinkle a small amount of the pudding-like ground seed/aquafaba mush over the potatoes and work it in with my fingers until it’s well distributed. I use about the same volume I would if I were using yolks (meaning, if I were using 1 yolk/lb potatoes, I’d use a seed/aquafaba pudding volume equivalent of 1 actual yolk).
Finally, I work in the flour until it feels right (holds together well enough to be rolled into the dough snakes from which the gnocchi is cut).
I’m afraid I can’t provide measurement guidance as I cook by feel, smell, taste, and never measure anything (unless I’m baking). I vary my recipe depending on intended use.
For example, if I want an ultra fluffy gnocchi for a light dish, I’ll use old dry potatoes and very little flour. If, on the other hand, I want to bake uncooked gnocchi in a sauce, I’ll increase the flour so that they hold together during a long submerged baking (this is a great thing to try with larger gnocchi baked in a marinara sauce).
Anyway, just have fun. Gnocchi is very forgiving. You can just make small batches and play around with proportions and egg substitutes until you nail it down.