I always ate onions on keto (along with carrots and peas, there were essential in my soups), it was among the 2 vegs I didn’t stop to eat when I went to carnivore-ish
No problem with the carb content at all. Of course, I don’t eat it like in my childhood but almost no one uses onions in that big amount
My scrambled eggs were more like eggy fried onions 
Onion is very, very flavorful, a tiny bit goes a long way! It’s very, very sweet too, for me and now so I almost never touch it as I dislike sugar in my savory dishes.
Did you look up garlic? That’s even carbier. And people use even less of it so no problem.
I drink as much milk as I wish too as I don’t care about animal carbs, they don’t seem to matter to me, just like the not net carbs 
It’s very easy to live without vegs if you ask me NOW. 5 years ago I would have said I can give up everything, even my darling eggs and adorable fruits if I must - but not vegs. How wrong I was 
Of course, we all have our limits and we need to be ready for certain jumps but it’s amazing how much we can change when it is about our food, among others!
What is “keto item”? You can eat ANYTHING on keto, there are no keto items and non-keto items, strictly… It’s not so advisable to eat very sugary food but I had plenty of them on keto as I could squeeze them in and considered them very important.
Meanwhile I had to ban cauliflower as it was way too carby even for my 40g net carb allowance. It’s about amounts… I could eat 10g frozen banana and considering it a perfect portion but I couldn’t eat little cauliflower (like 500g) at once. And the carbier items are usually WAY more flavorful so I got significantly less carbs if I used them instead of bland low-carb ones. Of course, it’s individual and some low-carb vegs are flavorful but it’s usually the sugary ones that made my soups tasty… I liked soups for various reasons, it’s very basic for us Hungarians, I grew up eating lots of soup every day but I liked them on keto because it was the only type of vegetable dishes that I could afford with my tiny, 40g net carb limit (without trying to eat just a bit, I can’t do that with vegs)… Vegetables are carby, I had to be very careful with them.
If I want to go below 20g carbs? (I don’t, it’s no special number for me but I do want to be very low most of the time.) Carnivore base, maybe with a tiny extra. IDK how people eat vegs below 20g carbs, honestly, I can’t. I need 3-20, sometimes 40g for the carni part of my diet alone… But yes, I could squeeze in some vegs if I wanted, I just don’t see the point anymore.