I too often make my own mayonnaise. I have tried it with soymilk and oil/vinegar, and I have made a tofu version, and several nut based versions (cashew is my favorite and my go to but I have also made an almond based mayonnaise). Avocado mayo is another one i have made and it works nicely for potato salad.
It used to be only the specialty health stores sold vegan mayo where I live, so for a long time I made my own because I didn't want to make the trek across town to get it. Then I started seeing Vegannaise appearing in mainstream groceries, and then Just Mayo arrived. My partner, who is omni, loves Just Mayo so much more than Hellmans and specifically buys it for himself. But he likes my homemade mayo the best (or he's just saying that so I don't rip his head off lol).