Where to find Veggie dumplings with spinach dough in NJ?
I think H-Mart is a great idea. 'Veggie' *if* it equals vegetarian is tricky with Chinese food in the US. (With packaged goods you can read the label.)
There are all kinds of vegetarians/pescaterians. I am the "I try my best, but if someone misunderstands me and it's already dead it's not my fault, so I'll try my best to eat it if I can" kinda guy. I know other people who sincerely feel it's like cannibalism so they have to be super pure. If you are in the latter group you might have to avoid dim-sum unless you go to vegetarian specific restaurants. [There is one in Chinatown (NYC) that I know of.]
In my experience, if you dig deep enough even fish and vegetable dishes, especially those which are dumplings, often have pork or animal fat. I go to dim sum and love it, knowing that I'm trying my best to avoid the stuff I don't eat, but if it ends up there, *shrug*, I did my best. (BTW - same thing with Thai, and why have thai if you don't enjoy fish sauce, imho.)
I also have shoes with some leather and coats with some down. I drive on roads that suffer from dead dear, skunk, groundhog, and other roadkill. I eat grains that are harvested that kill tons of insects. I don't think anyone is pure. I just try.
In short, authentic Chinese vegan/vegetarian is possible, but unlikely in NJ. You have to search out the outliers in NYC.